
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 an arithmetic sequence where the first four terms are $p$, $9$, $3p - q^3$, and $3p + q^3$. Find the $500^\text{th}$ term of this sequence.
A) $2003 - \sqrt[3]{2}$
B) $1996$
C) $2009$
D) $2005 - 2\sqrt[3]{2}$
E) $2009 + \sqrt[3]{2}$

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