
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 semicircle with radius 2021 has diameter \( AB \) and center \( O \). Points \( C \) and \( D \) lie on the semicircle such that \(\angle AOC < \angle AOD = 90^{\circ} \). A circle of radius \( r \) is inscribed in the sector bounded by \( OA \) and \( OC \) and is tangent to the semicircle at \( E \). If \( CD = CE \), compute \(\lfloor r \rfloor\).

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