
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
If \( F_{n} \) is an integral-valued function defined recursively by \( F_{n}(k) = F_{1}\left(F_{n-1}(k)\right) \) for \( n \geq 2 \) where \( F_{1}(k) \) is the sum of the squares of the digits of \( k \), find the value of \( F_{2012}(7) \).

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