
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
Triangle \( G R T \) has \( G R = 5 \), \( R T = 12 \), and \( G T = 13 \). The perpendicular bisector of \( G T \) intersects the extension of \( G R \) at \( O \). Find \( T O \).

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