
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
Given that the failure rate of each airplane engine during flight is $1 - P$, and the events of each engine failing are independent, and the airplane can successfully fly if at least $50\%$ of the engines are running normally, determine the range for the value of $P$ such that a four-engine airplane is safer than a two-engine airplane.

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