
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 worker retires with a pension that is proportional to the number of years they worked squared. Had the worker worked $2a$ years more, their pension would increase by $2p$ dollars. Alternatively, if they worked $3b$ years more, their pension would increase by $3q$ dollars. Find the annual pension in terms of $a, b, p,$ and $q$.
A) $\frac{bp-2aq}{6ab}$
B) $-\frac{p-2q}{b-a}$
C) $\frac{2bp-aq}{ab}$
D) $-\frac{bp-2aq}{6ab}$

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