
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
Let $C=\{ (i,j)|i,j$  integers such that  $0\leq i,j\leq 24\}$ How many squares can be formed in the plane all of whose vertices are in  $C$  and whose sides are parallel to the  $X-$ axis and  $Y-$  axis?

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