
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 beach resort is located \(400\) yards from a straight highway. Along this highway, a shopping mall is \(700\) yards away from a point on the highway directly opposite to the resort. It is planned to build a coffee shop on the highway equidistant from both the resort and the mall. Find the distance from the coffee shop to both the resort and the mall.
A) \(300\) yards
B) \(464\) yards
C) \(500\) yards
D) \(600\) yards
E) \(700\) yards

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