
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
Given a square  $ABCD,$  with  $AB=1$  mark the midpoints  $M$  and  $N$  of  $AB$  and  $BC,$  respectively. A lasar beam shot from  $M$  to  $N,$  and the beam reflects of  $BC,CD,DA,$  and comes back to  $M.$  This path encloses a smaller area inside square  $ABCD.$  Find this area. 

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