
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 function \( f(x) = \frac{1+x}{2-x} \), and for \( n \in \mathbf{N}_{+} \), define \( f_{1}(x) = f(x) \) and \( f_{n+1}(x) = f\left[f_{n}(x)\right] \). If \( f_{13}(x) = f_{31}(x) \), what is the expression for \( f_{16}(x) \)?

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