
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
If  $x_0=x_1=1$ , and for  $n\geq1$  $x_{n+1}=\frac{x_n^2}{x_{n-1}+2x_n}$ ,

find a formula for  $x_n$  as a function of  $n$ .

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