
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 $f(x) = \begin{cases} |x-1|-2 & \text{if } |x| \leq 1 \\ \frac{1}{1+x^2} & \text{if } |x| > 1 \end{cases}$. Evaluate the value of $f\left[f\left(\frac{1}{2}\right)\right]$.

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