
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
In a rectangle  $ABCD$ , let  $M$  and  $N$  be the midpoints of sides  $BC$  and  $CD$ , respectively, such that  $AM$  is perpendicular to  $MN$ . Given that the length of  $AN$  is  $60$ , the area of rectangle  $ABCD$  is  $m \sqrt{n}$  for positive integers  $m$  and  $n$  such that  $n$  is not divisible by the square of any prime. Compute  $100m+n$ .

*Proposed by Yannick Yao*

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