
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
The bisector of angle  $A$  in parallelogram  $ABCD$  intersects side  $BC$  at  $M$  and the bisector of  $\angle AMC$  passes through point  $D$ . Find angles of the parallelogram if it is known that   $\angle MDC = 45^o$ .
![Image](https://cdn.artofproblemsolving.com/attachments/e/7/7cfb22f0c26fe39aa3da3898e181ae013a0586.png)

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