
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 girl's camp is located $400$ rods from a straight road at an angle of $30^\circ$ to the perpendicular from the road, and a boy's camp is located $600$ rods directly from the girl's camp along a line that intersects the road at a $90^\circ$ angle. Find the closest distance from the road where a canteen can be built that is equidistant from both camps.

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