
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
A circular disk is divided by $3n$ equally spaced radii and two secant lines that do not intersect at the disk's center. Determine the maximum number of non-overlapping areas into which the disk can be divided.
A) $4n$
B) $4n + 2$
C) $6n + 1$
D) $8n + 1$
E) $10n + 2$

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