
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 vertical fence of height $m$ meters is located $f$ meters from a vertical wall. We need to position a ladder of $h$ meters such that it leans against the wall, touches the ground, and rests on the top of the fence. Determine the distance from the ground to the point where the ladder leans against the wall, accurate to the nearest centimeter. 

Example: $m=f=5$ meters, $h=15$ meters.

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