
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 rock is dropped off a cliff of height $h$. As it falls, a camera takes several photographs, at random intervals. At each picture, you measure the distance the rock has fallen. Let the average (expected value) of all these distances be $kh$. If the number of photographs taken is huge, find $k$.

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