
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
Given a line $f$ and two parallel lines $e$ and $g$ that are each at a unit distance from $f$ on either side. Let points $E$, $F$, and $G$ be on lines $e$, $f$, and $g$ respectively, such that the triangle formed by $E$, $F$, and $G$ has a right angle at $F$. What is the length of the altitude of the triangle from point $F$?

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