
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
When some number  $a^2$  is written in base  $b$ , the result is  $144_b$ .  $a$  and  $b$  also happen to be integer side lengths of a right triangle. If  $a$  and  $b$  are both less than  $20$ , find the sum of all possible values of  $a$ .


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