
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 of radius \(R\) at points \(A\) and \(B\) such that \(\angle AOB = 45^\circ\). The line also intersects another line perpendicular to the diameter \(AM\) of the circle and passing through its center at point \(K\). The line passing through point \(B\) and perpendicular to \(AM\) intersects \(AM\) at point \(C\). Find the area of the trapezoid \(OCBK\).

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