
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 an acute-angled $\triangle DEF$ inscribed in a circle with center $O$, $\stackrel \frown {DE} = 160^\circ$ and $\stackrel \frown {EF} = 56^\circ$. A point $G$ is chosen on the minor arc $DF$ such that $OG$ is perpendicular to $DF$. Find the ratio of the magnitudes of $\angle OGF$ and $\angle DEF$.

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