
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
Observe the following equations:

\\(①\\cos 2\\)_\\(α\\)_\\(=2\\cos ^{2}\\)_\\(α\\)_\\(-1\\)
\\(②\\cos 4\\)_\\(α\\)_\\(=8\\cos ^{4}\\)_\\(α\\)_\\(-8\\cos ^{2}\\)_\\(α\\)_\\(+1\\)
\\(③\\cos 6\\)_\\(α\\)_\\(=32\\cos ^{6}\\)_\\(α\\)_\\(-48\\cos ^{4}\\)_\\(α\\)_\\(+18\\cos ^{2}\\)_\\(α\\)_\\(-1\\)
\\(④\\cos 8\\)_\\(α\\)_\\(=128\\cos ^{8}\\)_\\(α\\)_\\(-256\\cos ^{6}\\)_\\(α\\)_\\(+160\\cos ^{4}\\)_\\(α\\)_\\(-32\\cos ^{2}\\)_\\(α\\)_\\(+1\\)
\\(⑤\\cos 10\\)_\\(α\\)_\\(=\\)_\\(m\\)_\\(\\cos ^{10}\\)_\\(α\\)_\\(-1 280\\cos ^{8}\\)_\\(α\\)_\\(+1 120\\cos ^{6}\\)_\\(α\\)_\\(+\\)_\\(n\\)_\\(\\cos ^{4}\\)_\\(α\\)_\\(+\\)_\\(p\\)_\\(\\cos ^{2}\\)_\\(α\\)_\\(-1\\)

We can infer that \_(n)_\_(p)_\_ = \_\_\_\_\_\_\_\_.

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