
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 integer  $x\in\{1,\dots,102\}$  is  $\textit{square-ish}$  if there exists some integer  $n$  such that  $x\equiv n^2+n\pmod{103}$ . Compute the product of all  $\textit{square-ish}$  integers modulo  $103$ .

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