
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 retired worker receives an annual pension that is proportional to the square root of the number of years they served. If they serve $a$ additional years, their pension increases by $p$ dollars. If they serve $b$ additional years $(b \neq a)$, their pension increases by $q$ dollars. Express their annual pension in terms of $a$, $b$, $p$, and $q$.

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