
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
There is a question written on the blackboard: $2\square (-\frac{1}{2})$. Fill in the "$\square$" with one of the four arithmetic operators: "$+$", "$-$", "$\times$", or "$\div$".<br/>$(1)$ Find the probability that the result of the operation is negative;<br/>$(2)$ If the teacher randomly selects two arithmetic operators to substitute into the operation, find the probability that the results of both operations are negative.

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