
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
If for any $x\in A$, we have $\frac{1}{x}\in A$, then the set $A$ is called a "harmonious" set. What is the probability of "harmonious" sets among all non-empty subsets of the set $M=\{-1,0, \frac{1}{3}, \frac{1}{2},1,2,3,4\}$?

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