
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 $f(x)=\begin{cases} 3^{x}-1, & x>0 \\ x^{2}+1, & x\leq0 \end{cases}$, find the minimum value of $x_{1}$ for which $f(x_{1}) = f(x_{2})$, where $x_{1} \in (0, +\infty)$ and $x_{2} \in (-\infty, 0]$.

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