
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
Two camps, one for girls and another for boys, are located near a straight road. The girls' camp is located 400 rods perpendicular from the road. The boys' camp is along the road at a point 800 rods away from the perpendicular dropped from the girls' camp onto the road. It is desired to build a shop on the road so that it is equidistant from both camps. Find the distance from the shop to each of the camps.
A) 100 rods
B) 300 rods
C) 500 rods
D) 700 rods
E) 900 rods

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