
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
In a simulated airplane shooting game, Xiao Li fired twice in succession. Let proposition $p_1$ be "the first shot hit the airplane", and proposition $p_2$ be "the second shot hit the airplane". Use $p_1$, $p_2$, and the connectives "or", "and", "not" to express the following propositions:  
(1) Both shots hit the airplane;  
(2) Both shots missed the airplane;  
(3) Exactly one shot hit the airplane;  
(4) At least one shot hit the airplane.

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