
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
Find \( \cot G \) in the right triangle shown below.

[asy]

pair H,F,G;

H = (0,0);

G = (12,0);

F = (0,5);

draw(F--G--H--F);

draw(rightanglemark(F,H,G,20));

label("$H$",H,SW);

label("$G$",G,SE);

label("$F$",F,N);

label("$13$",(F+G)/2,NE);

label("$12$",G/2,S);

[/asy]

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