
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
Let  $ABC$  be a triangle with  $\angle BAC=40^\circ $ ,  $O$  be the center of its circumscribed circle and  $G$  is its centroid. Point  $D$  of line  $BC$  is such that  $CD=AC$  and  $C$  is between  $B$  and  $D$ . If  $AD\parallel OG$ , find  $\angle ACB$ .

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