
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 \( S_7 \) denote all the permutations of \(1, 2, \ldots, 7\). For any \(\pi \in S_7\), let \( f(\pi) \) be the smallest positive integer \( i \) such that \(\pi(1), \pi(2), \ldots, \pi(i)\) is a permutation of \(1, 2, \ldots, i\). Compute \(\sum_{\pi \in S_7} f(\pi)\).

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