
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
On the extension of side $BC$ of an equilateral triangle $ABC$, a point $M$ is chosen. Through this point, a line is drawn parallel to $AC$. This line intersects the extension of side $AB$ at point $N$. The medians of triangle $BNM$ intersect at point $O$. Point $D$ is the midpoint of $AM$. Find the angles of triangle $ODC$.

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