
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 $(p, q, r, s)$ be a solution to the system:
\begin{align*}
p + q &= 18, \\
pq + r + s &= 85, \\
pr + qs &= 190, \\
rs &= 120.
\end{align*}
Find the greatest possible value of $p^2 + q^2 + r^2 + s^2$.

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