
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 a function \( f(x) \) that is defined on the set of real numbers \( \mathbb{R} \) and is an odd function, and another function \( g(x) = f(x+2) \) that is an even function, with \( f(x) = x \) when \( x \in [0, 2] \), determine the number of such functions \( f(x) \).

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