
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 \(\triangle ABC\) be an isosceles right triangle with \(AB = AC = 10\). Let \(M\) be the midpoint of \(BC\) and \(N\) the midpoint of \(BM\). Let \(AN\) intersect the circumcircle of \(\triangle ABC\) again at \(T\). Compute the area of \(\triangle TBC\).

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