
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
Given the number $825$, convert it into a factorial base of numeration, that is, $825 = a_1 + a_2 \times 2! + a_3 \times 3! + \dots + a_n \times n!$ where $0 \le a_k \le k$. Find the value of $a_5$.

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