
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 \(a\), \(b\), and \(c\) be the lengths of the three sides of a triangle. Suppose \(a\) and \(b\) are the roots of the equation
\[
x^2 + 4(c + 2) = (c + 4)x,
\]
and the largest angle of the triangle is \(x^\circ\). Find the value of \(x\).

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