
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
For any positive integer $n$, the value of $n!$ is the product of the first $n$ positive integers. For example, $6! = 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1 = 720$. What is the greatest common divisor of $8!$ and $10!$?

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