
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
Assume the failure rate of each engine during flight is $1-p$, and the failure of engines is independent. It is known that if at least 3 out of 4 engines are functioning, the airplane can fly successfully. For a 2-engine airplane, both engines must be functioning for it to fly successfully. If a 4-engine airplane is safer than a 2-engine airplane, determine the range of $p$.

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