
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
In triangle \( XYZ \), \( XY = 10 \). The length of median \( XT \) from vertex \( X \) to \( YZ \) is 7. Let \( N \) be the largest possible value of \( XZ^2 + YZ^2 \), and let \( n \) be the smallest possible value. Find \( N - n \).

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