
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
Let \( G_1 G_2 G_3 \) be a triangle with \( G_1 G_2 = 7 \), \( G_2 G_3 = 13 \), and \( G_3 G_1 = 15 \). Let \( G_4 \) be a point outside triangle \( G_1 G_2 G_3 \) so that ray \( \overrightarrow{G_1 G_4} \) cuts through the interior of the triangle, \( G_3 G_4 = G_4 G_2 \), and \( \angle G_3 G_1 G_4 = 30^\circ \). Let \( G_3 G_4 \) and \( G_1 G_2 \) meet at \( G_5 \). Determine the length of segment \( G_2 G_5 \).

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