
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  $f(x) = 1 + \frac{2}{x}$ . Put  $f_1(x) = f(x)$ ,  $f_2(x) = f(f_1(x))$ ,  $f_3(x) = f(f_2(x))$ ,  $... $ . Find the solutions to  $x = f_n(x)$  for  $n > 0$ .	

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