
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
Consider function $g$ that satisfies $g(x+6) + g(x-6) = 2g(x)$ and $g$ is an even function, for all real $x$. Assuming $g$ is periodic, find the least positive period $p$ of $g$.
**A)** 18
**B)** 24
**C)** 30
**D)** 36
**E)** 48

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