
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 we call $A$ a "harmonic" set. What is the probability that a non-empty subset of the set $M=\left\{ -1,0,\frac{1}{3},\frac{1}{2},1,2,3,4 \right\}$ is a "harmonic" set?

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