
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 $f(x)= \begin{cases} 2^{-x}-1,x\leqslant 0 \\ x^{ \frac {1}{2}},x > 0\\ \end{cases}$, if $x$ satisfies $f(x)\geqslant 3$, then the maximum value of $\log _{2}( \frac {x+1}{x-1})$ is ___.

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