
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
Given a circle with a unit radius centered at O. Point \( A \) is at a distance \( a \) from the center ( \( 0 < a < 1 \) ). Through point \( A \), all possible chords \( MN \) are drawn.
a) Find the length of the shortest chord \( MN \).
b) Find the maximum area of the triangle \( OMN \).

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