
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 \(ABCDEF\) has a side length of 2. A laser beam is fired inside the hexagon from point \(A\) and hits line segment \(\overline{BC}\) at point \(G\). The laser then reflects off \(\overline{BC}\) and hits the midpoint of \(\overline{DE}\). Find the length of \(BG\).

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