
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
ABC is an equilateral triangle with a side length of 10. A point D is taken on side AB, a point E on side AC, and points F and G on side BC such that triangles ADE, BDG, and CEF are also equilateral. AD = 3. Find FG.

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