
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 $\tan(x+ \frac {\pi}{4})= \frac {1+\tan x}{1-\tan x}$, y=tanx has a period $T=\pi$, and the function y=f(x) satisfies $f(x+a)= \frac {1+f(x)}{1-f(x)}$ for $x\in\mathbb{R}$ (where $a$ is a non-zero constant), find the period of the function y=f(x).

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