
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
Find all functions \( f : [1, +\infty) \rightarrow [1, +\infty) \) that satisfy the following conditions:
1. \( f(x) \leq 2(x + 1) \);
2. \( f(x + 1) = \frac{1}{x} \left[ (f(x))^2 - 1 \right] \).

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