
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 &= 18, \\
ab + c + d &= 85, \\
ad + bc &= 180, \\
cd &= 104.
\end{align*}
Find the smallest possible value of \(a^2 + b^2 + c^2 + d^2\).

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