
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 $p,$ $q,$ $r,$ and $w$ be complex numbers such that $|p| = |q| = |r| > 0$ and 
\[pw^3 + qw^2 + rw + r = 0.\] 
Find the largest possible value of $|w|$.

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