
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
Kelvin the Frog lives in the 2-D plane.  Each day, he picks a uniformly random direction (i.e. a uniformly random bearing  $\theta\in [0,2\pi]$ ) and jumps a mile in that direction.  Let  $D$  be the number of miles Kelvin is away from his starting point after ten days.  Determine the expected value of  $D^4$ .  

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