Chained && and || operators in bash scripting - linux

Question

I want to execute a series of commands in a bash script.
If any fail, the script should echo a line describing which line failed, and then exit the function.
Currently, my script echos the output adequately, but doesn't exit the script (because the echo command returns 0).
I have
COMMAND_A || echo "command A failed" | tee -a $SUMMARY_FILE
COMMAND_B || echo "command B failed" | tee -a $SUMMARY_FILE
COMMAND_C || echo "command C failed" | tee -a $SUMMARY_FILE
but these have no dependence on the previous line - I think enclosing with bash -e would also not help, since then either COMMAND_A failing would exit without the echo, or else the echo would succeed and nothing would exit.
Since the echo will succeed, I can't just add && to each line.
I could perhaps use
{ COMMAND_A && \
{ COMMAND_B && \
{ COMMAND_C || echo "C failed" | tee -a $SUM } \
|| echo "B failed" | tee -a $SUM } \
|| echo "A failed" | tee -a $SUM }
but this seems very clunky.
Is there a better syntax/style/method?
For a concrete example:
cmake -DCMAKE_INSTALL_PREFIX=$PREFIX -DCMAKE_BUILD_TYPE=Release .. || \
echo "$(date +%d/%m/%y-%H:%M:%S): cmake failed for $1" | tee -a $SUMFILE
make -j16 || \
echo "$(date +%d/%m/%y-%H:%M:%S): make failed for $1" | tee -a $SUMFILE
sudo make install && \
echo "$(date +%d/%m/%y-%H:%M:%S): Installed $1" | tee -a $SUMFILE || \
echo "$(date +%d/%m/%y-%H:%M:%S): make install failed for $1" | tee -a $SUMFILE
Edit
I can perhaps get some improvement with
COMMAND_A || { echo "A failed" && false; } && \
COMMAND_B || { echo "B failed" && false; } && \
COMMAND_C && echo "C succeeded" || { echo "C failed" && false; }
but this will still print that A, B and C failed if A fails (even though the commands are short-circuited, hence the improvement)

Answer 1

Since the series of commands is executed within a function, the return statement can be used.
If this were not the case, exit may be the appropriate choice.
Consequently, I can use the idea in the question's edit to write:
standardInstall() {
# Should be passed the directory (ie application/library) name as
# an argument.
if [ -z "$1" ]; then
echo "No argument was passed to standardInstall()"
echo "Exiting"
exit 2
fi
pushd $1/build/
cmake -DCMAKE_INSTALL_PREFIX=$KF5 -DCMAKE_BUILD_TYPE=Release .. || \
{ echo "$(date +%d/%m/%y-%H:%M:%S): cmake failed for $1" \
| tee -a $SUMFILE && return 1; } && \
make -j16 || \
{ echo "$(date +%d/%m/%y-%H:%M:%S): make failed for $1" \
| tee -a $SUMFILE && return 1; } && \
sudo make install && \
echo "$(date +%d/%m/%y-%H:%M:%S): Installed $1" | tee -a $SUMFILE || \
{ echo "$(date +%d/%m/%y-%H:%M:%S): make install failed for $1" \
| tee -a $SUMFILE && return 1; }
popd
}