
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
Let $O$ be the origin, and let $(a,b,c)$ be a fixed point. A cylinder passes through $(a,b,c)$ with its axis parallel to the z-axis. It intersects the $x$-axis and $y$-axis at points $A$ and $B$, respectively. If $(p,q)$ is the center of the circular base of the cylinder, find:
\[\frac{a}{p} + \frac{b}{q}.\]

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