
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 probability of an engine failure during flight for each airplane is $1-p$, and the occurrences of failure for each engine are independent. It is known that a four-engine airplane can successfully fly if at least three engines are operating normally, and a two-engine airplane requires both engines to be operating normally to successfully fly. Determine the range of values for $p$ when a four-engine airplane is safer than a two-engine airplane.

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