
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

...

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system
In the diagram, \( OAB \) is a quarter circle, \( OE \) and \( CD \) are parallel, \( BC \) and \( EA \) are parallel, and \( \angle BCD = 4 \times \angle OBC \). What is the size of \( \angle OBC \)?

Given:
- Quadrilateral \( FCGE \) must be a parallelogram since \( OE \) is parallel to \( CD \) and \( BC \) is parallel to \( EA \).
- \( \angle BCD = \angle AEO = 4x^\circ \).
- Triangle \( OAE \) is isosceles with \( OA = OE \), both being radii of the quarter circle \( OAB \), thus \( \angle OAE = \angle AEO = 4x^\circ \).
- \( \angle OCB = \angle OAE \) due to corresponding angles since \( BC \) is parallel to \( EA \).
- \( OAB \) being a quarter circle gives \( \angle BOA = 90^\circ \).

Consider the sum of the interior angles of the right-angled triangle \( OCB \):
\[ 180^\circ = 90^\circ + 4x^\circ + x^\circ \]

Solving the equation:
\[ 90^\circ = 5x^\circ \]

Therefore:
\[ \angle OBC = x^\circ = 18^\circ \]

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