
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 $x_1, x_2, \ldots, x_{10}$ be a permutation of $1, 2, \ldots, 10$. Find the number of different permutations such that for any positive integers $m, n$ with $1 \leq m < n \leq 10$, the inequality $x_m + m \leq x_n + n$ holds.

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