
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 regular hexagon with side length  $1$  is given. Using a ruler construct points in such a way that among the given and constructed points there are two such points that the distance between them is  $\sqrt7$ .

Notes: ''Using a ruler construct points  $\ldots$ '' means: Newly constructed points arise only as the intersection of straight lines connecting two points that are given or already constructed. In particular, no length can be measured by the ruler.

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