
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
Let \( n! = 1 \times 2 \times \cdots \times n \) and \([x]\) represent the greatest integer less than or equal to the real number \( x \). Then the equation
$$
\left[\frac{x}{1!}\right] + \left[\frac{x}{2!}\right] + \cdots + \left[\frac{x}{10!}\right] = 3468
$$
has a positive integer solution of \(\qquad\)

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