
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]


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Given positive real numbers $x_{1}$, $x_{2}$ and the function $f(x)$ satisfying $4^{x}=\frac {1+f(x)}{1-f(x)}$, and $f(x_{1})+f(x_{2})=1$, determine the minimum value of $f(x_{1}+x_{2})$.

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