
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 \( f(x)=\left\lfloor\frac{x}{1!}\right\rfloor+\left\lfloor\frac{x}{2!}\right\rfloor+\cdots+\left\lfloor\frac{x}{2013!}\right\rfloor \) (where \( \left\lfloor x \right\rfloor \) denotes the greatest integer not exceeding the real number \( x \)). For an integer \( n \), if the equation \( f(x)=n \) has a real solution for \( x \), then \( n \) is called a "good number". Find the number of good numbers in the set \(\{1, 3, \cdots, 2013\}\).

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