
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 2α=2\\cos ^{2}α-1\\)；
\\(②\\cos 4α=8\\cos ^{4}α-8\\cos ^{2}α+1\\)；
\\(③\\cos 6α=32\\cos ^{6}α-48\\cos ^{4}α+18\\cos ^{2}α-1\\)；
\\(④\\cos 8α=128\\cos ^{8}α-256\\cos ^{6}α+160\\cos ^{4}α-32\\cos ^{2}α+1\\)；
\\(⑤\\cos 10α=m\\cos ^{10}α-1280\\cos ^{8}α+1120\\cos ^{6}α+n\\cos ^{4}α+p\\cos ^{2}α-1\\)；
We can infer that, \\(m-n+p=\\) \_\_\_\_\_\_.

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