
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
451986 can be written in the form: $1986 = a_{1} + a_{2} \cdot 2! + a_{3} \cdot 3! + \cdots + a_{n} \cdot n!$, where $a_{k}$ are integers and $0 \leq a_{k} \leq k$ (for $k=1, 2, 3, \cdots, n$). Find the values of $a_{k}$.

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