
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
It is known that the number \(\cos 6^{\circ}\) is a root of the equation \(32 t^{5} - 40 t^{3} + 10 t - \sqrt{3} = 0\). Find the other four roots of this equation. (The answers should be in compact expressions that do not contain summation signs, ellipses, or radicals.)

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