
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 the triangular diagram shown, suppose $\cos M = \frac{3}{5}$. If LM measures 15 units, find the length of LN.

[asy]
pair L,M,N;
M = (0,0);
N = (20,0);
L = (0,15);
draw(L--M--N--L);
draw(rightanglemark(L,M,N,15));
label("$M$",M,SW);
label("$N$",N,SE);
label("$L$",L,NE);
label("$15$",L/2,W);
[/asy]

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