
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
\[p^3 - 21p^2 + 35p - 105 = 0 \quad \text{and} \quad 5q^3 - 35q^2 - 175q + 1225 = 0.\]
Compute \(p + q.\)

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