
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 $f(x) = \begin{cases} \frac{1}{2} - \frac{2}{e^{x}+1}, & x\geq 0 \\ \frac{2}{e^{x}+1} - \frac{3}{2}, & x<0 \end{cases}$  
(1) Find the zeros of the function $f(x)$.  
(2) If the real number $t$ satisfies $f(\log_{2}t) + f(\log_{2}\frac{1}{t}) < 2f(2)$, find the range of $f(t)$.

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