
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
The CMU Kiltie Band is attempting to crash a helicopter via grappling hook.  The helicopter starts parallel (angle  $0$  degrees) to the ground.  Each time the band members pull the hook, they tilt the helicopter forward by either  $x$  or  $x+1$  degrees, with equal probability, if the helicopter is currently at an angle  $x$  degrees with the ground.  Causing the helicopter to tilt to  $90$  degrees or beyond will crash the helicopter.  Find the expected number of times the band must pull the hook in order to crash the helicopter.

*Proposed by Justin Hsieh*

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