
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 points  $M$  and  $N$  are located respectively on the diagonal  $(AC)$  and the side  $(BC)$  of the square  $ABCD$  such that  $MN = MD$ . Determine the measure of the angle  $MDN$ .

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