
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 that $\tan(x + \frac{π}{4}) = \frac{1 + \tan x}{1 - \tan x}$, the period of $y = \tan x$ is $T = π$, and the function $y = f(x)$ satisfies $f(x + a) = \frac{1 + f(x)}{1 - f(x)}$, $x \in \mathbb{R}$ ($a$ is a non-zero constant), determine the period of the function $y = f(x)$.

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