
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 \((a,b,c,d)\) be a solution to the system
\begin{align*}
a+b &= 17, \\
ab+c+d &= 94, \\
ad+bc &= 195, \\
cd &= 120.
\end{align*}
Find the greatest possible value of \(a^2+b^2+c^2+d^2\).

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