
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
In a circle with center $O$, an acute-angled $\triangle ABC$ is inscribed such that $\stackrel \frown {AB} = 140^\circ$ and $\stackrel \frown {BC} = 40^\circ$. A point $D$ is placed on the minor arc $AC$ so that $OD$ is perpendicular to $AC$. Calculate the ratio of the magnitudes of $\angle OBD$ and $\angle BAC$.

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