
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 \( D = \{ 1, 2, \ldots, 10 \} \). The function \( f(x) \) is a bijection from \( D \) to \( D \). Define \( f_{n+1}(x) = f(f_n(x)) \) for \( n \in \mathbf{N}_+ \) and \( f_1(x) = f(x) \). Find a permutation \( x_1, x_2, \ldots, x_{10} \) of \( D \) such that \( \sum_{i=1}^{10} x_i f_{2520}(i) = 220 \).

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