
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:
\[ p^3 - 18p^2 + 27p - 135 = 0 \quad \text{and} \quad 12q^3 - 90q^2 - 450q + 4950 = 0. \]
Compute \( p + q. \)

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