
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The number $A1B\,CDE\,FGH\,IJK$ is divisible by $144.$ If $F$, $G$, $H$, and $J$ each represent a single digit, what is the sum of all distinct possible values of the product $FGHJ?$ (Count each possible value of $FGHJ$ only once, even if it results from multiple $F$, $G$, $H$, $J$ pairs.)

Present the answer in LaTex format: \boxed{Your answer}
user