
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 \( d_{1}, d_{2}, \ldots, d_{n} \) be all the natural divisors of the number \( 10! = 1 \cdot 2 \cdot \ldots \cdot 10 \). Find the sum

$$
\frac{1}{d_{1}+\sqrt{10!}}+\frac{1}{d_{2}+\sqrt{10!}}+\ldots+\frac{1}{d_{n}+\sqrt{10!}}
$$

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