
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
Suppose $a$, $b$, and $c$ are positive integers such that $a+b+c=2010$ and $b = 2a$. If $a!b!c! = m \cdot 10^n$ where $m$ and $n$ are integers and $m$ is not divisible by 10, what is the smallest possible value of $n$?
A) 586
B) 589
C) 592
D) 595
E) 598

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