
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
Acute-angled $\triangle ABC$ is inscribed in a circle with center at $O$; $\stackrel \frown {AB} = 100^\circ$ and $\stackrel \frown {BC} = 50^\circ$.
A point $E$ is taken on the minor arc $AC$ such that $OE$ is perpendicular to $AC$. Find the ratio of the magnitudes of $\angle OBE$ and $\angle BAC$.

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