
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:
$$f(x)= \begin{cases} 2e^{x-1}, & \text{if } x<2 \\ \log_{3}(x^{2}-1), & \text{if } x\geq 2. \end{cases}$$
Find the value of $f(f(2))$.

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