
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
The number $1050$ is to be written with a factorial base of numeration, that is, $1050=a_1+a_2\times2!+a_3\times3!+ \ldots a_n \times n!$ where $0 \le a_k \le k,$ and $n!$ means $n(n-1)(n-2)...2 \times 1$. Find $a_5$.
A) 0
B) 1
C) 2
D) 3
E) 4

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