
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
Given the sequence \( a_{1}, a_{2}, a_{3}, \cdots, a_{n}, \cdots \) with \( n \geqslant 1 \) and \( a_{i} \in \mathbf{N}^{*} \), and the relation \( a_{a_{n}} + a_{n} = 2n \), find \( a_{1}, a_{2}, \ldots, a_{n} \).

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