
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 $p$ and $q$ be real numbers such that
\[p^3 - 18p^2 + 27p - 72 = 0 \quad \text{and} \quad 10q^3 - 75q^2 + 50q - 625 = 0.\]Compute $p + q.$

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