
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 $1036$ represented in factorial base numeration as $1036 = b_1 + b_2 \times 2! + b_3 \times 3! + \ldots + b_n \times n!$, where each $b_k$ satisfies $0 \leq b_k \leq k$, find the value of $b_4$.

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