
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 \( \triangle ABC \), \( \angle A = 90^\circ \), \( \angle B = 45^\circ \), and \( \angle C = 45^\circ \). Circle with center \( O \) is tangent to side \( AC \) at point \( M \) and extends outside to tangent \( AB \) at point \( N \). If \( O \) is also the midpoint of \( BC \), find the length of \( BC \) if \( AM = 10 \) units.
A) \( 10 \)
B) \( 20 \)
C) \( 20\sqrt{2} \)
D) \( 40 \)

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