
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
In a regular heptagon (7-sided polygon) where $a$, $c$, and $d$ represent the side length, the length of a diagonal spanning two sides, and the length of a diagonal spanning three sides respectively, determine the correct relationship between these lengths.
A) $d = c + a$
B) $d^2 = c^2 + a^2$
C) $c^2 = a^2 + d^2$
D) $d^2 = 2c^2 - a^2$

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