
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 product \(1 \times 2 \times 3 \times \cdots \times n\) is denoted by \(n!\). For example, \(4! = 1 \times 2 \times 3 \times 4 = 24\). Let \(M = 1! \times 2! \times 3! \times 4! \times 5! \times 6! \times 7! \times 8! \times 9!\). How many factors of \(M\) are perfect squares?

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