
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
Consider the function \( f \) defined by
\[ f(x) = 1 + \frac{2}{x}. \]

Find the roots of the equation
\[ (\underbrace{f \circ f \circ \cdots \circ f}_{10 \text{ times }})(x) = x, \]
where "o" denotes composition of functions.

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