
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 $x \in A$, then $\frac{1}{x} \in A$, we call $A$ a "harmonic" set. Then, among all non-empty subsets of the set $M=\{-1, 0, \frac{1}{3}, \frac{1}{2}, 1, 2, 3, 4\}$, the probability of being a "harmonic" set is \_\_\_\_\_\_.

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