
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
We know the following about five points on a plane:

a) Three points form an equilateral triangle.

b) The remaining two points are symmetric with respect to one of the triangle's axes. Their distance from each other is 1 unit, and their distance from the point on the axis is $\sqrt{7}$ units.

c) One element of each pair of symmetric points is 2 units away.

What is the side length of the equilateral triangle?

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