
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
Triangle  $ABC$  has a right angle at  $C$ , and  $D$  is the foot of the altitude from  $C$  to  $AB$ . Points  $L, M,$  and  $N$  are the midpoints of segments  $AD, DC,$  and  $CA,$  respectively. If  $CL = 7$  and  $BM = 12,$  compute  $BN^2$ .

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