
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 $\cos 2\alpha = 2\cos^2\alpha - 1$;  
② $\cos 4\alpha = 8\cos^4\alpha - 8\cos^2\alpha + 1$;  
③ $\cos 6\alpha = 32\cos^6\alpha - 48\cos^4\alpha + 18\cos^2\alpha - 1$;  
④ $\cos 8\alpha = 128\cos^8\alpha - 256\cos^6\alpha + 160\cos^4\alpha - 32\cos^2\alpha + 1$;  
⑤ $\cos 10\alpha = m\cos^{10}\alpha - 1280\cos^8\alpha + 1120\cos^6\alpha + n\cos^4\alpha + p\cos^2\alpha - 1$;  
It can be inferred that $m - n + p =$ __ .

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