
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
Express the number $700$ in a factorial base of numeration, that is, $700=a_1+a_2\times2!+a_3\times3!+a_4\times4!+ \ldots a_n \times n!$ where $0 \le a_k \le k,$ for each $k$. Find the coefficient $a_4$.

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