
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
For a certain angle \( x \), the equation

\[ a \cos^2 x + b \cos x + c = 0 \]

is satisfied. Write the quadratic equation that \( \cos 2x \) satisfies. Apply your result to the case when \( a = 4 \), \( b = 2 \), and \( c = -1 \).

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