
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 circular disk divided into $2n+1$ equally spaced chords and by two intersecting secant lines that both pass through the center, calculate the maximum number of non-overlapping regions into which the disk can be divided. Assume \( n > 0 \).
A) \( 4n + 2 \)
B) \( 6n + 3 \)
C) \( 8n + 8 \)
D) \( 10n + 5 \)

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