
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 non-empty set M that satisfies M⊆{0，1，2，…n} (n≥2, n∈N+), if there exists a non-negative integer k (k≤n) such that when a∈M, it follows that 2k-a∈M, then the set M is said to have property P. Let f(n) denote the number of sets with property P. Find the value of f(9) - f(8).

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