
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 $f(x) = \begin{cases} \sqrt{x}, & 0 < x < 1 \\ 2(x-1), & x \geq 1 \end{cases}$, if $f(a) = f(a+1)$, calculate $f\left( \frac{1}{a} \right)$.

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