
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
A line intersects a circle with radius \( R \) at points \( A \) and \( B \) such that the measure of arc \( \overset{\frown}{AB} = 45^\circ \). Additionally, a line perpendicular to the diameter \( AM \) of the circle and passing through its center intersects the first line at point \( D \). The line passing through point \( B \) perpendicular to the diameter \( AM \) intersects \( AM \) at point \( C \). Find the area of the trapezoid \( OCBD \).

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