
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
We say that an ordered pair  $(a,b)$  of positive integers with  $a>b$  is square-ish if both  $a+b$  and  $a-b$  are perfect squares. For example,  $(17,8)$  is square-ish because  $17+8=25$  and  $17-8=9$  are both perfect squares. How many square-ish pairs  $(a,b)$  with  $a+b<100$  are there?

*Proposed by Nathan Xiong*

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