
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 positive integers  $ a$  and  $ b$  are such that the numbers   $ 15a \plus{} 16b$  and  $ 16a \minus{} 15b$  are both squares of positive integers. What is the least possible value that can be taken on by the smaller of these two squares?

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