
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
A manufacturer of airplane parts makes a certain engine that has a probability \( p \) of failing on any given flight. There are two planes that can be made with this sort of engine, one that has 3 engines and one that has 5 engines. A plane crashes if more than half its engines fail. For what values of \( p \) do the two plane models have the same probability of crashing?

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