
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&=85,\\
ad+bc&=180,\\
cd&=105.
\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