
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 diagram below, we have \( \cos \angle VTX = \frac{4}{5} \). What is \( \cos \angle VTU \)?

[asy]
pair V,T,X,U;
U = (-2,0);
T = (0,0);
X = (2,0);
V = rotate(aCos(4/5))*(1.5,0);
dot("$U$",U,S);
dot("$X$",X,S);
dot("$V$",V,N);
dot("$T$",T,S);
draw(X--U);
draw(T--V);
[/asy]

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