
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
Given a sequence {a_{n}} with a total of m terms, a_{1}=111, a_{2}=217, and for n∈N^*, 3≤n≤m, a_{n}=a_{n-2}−\frac{n-p}{a_{n-1}}. When the maximum value of the number of terms m is 220, find the value of the constant p.

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