
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 $f(x) = \frac{x^2}{2x+1}$, $f_1(x) = f(x)$, $f_n(x) = \overset{\overset{f(\cdots f(x)\cdots)}{}}{n\text{个}f}$, then $f_{10}\left(\frac{1}{2}\right) = \_\_\_\_\_\_$.

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