
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, what is the value of \( y \)? Enter the angle values as shown:
[asy]
draw(Arc((0,0),1,-120,42));

draw((-3,-3*sqrt(3))--(4,4*sqrt(3))--(4,-3*sqrt(3))--(-2*sqrt(3)/.8,-3*sqrt(3))--(4,3.6));
draw((3.6,-3*sqrt(3))--(3.6,-3*sqrt(3)+.4)--(4,-3*sqrt(3)+.4));
label("$72^\circ$",(4, 2),W);
label("$45^\circ$",(-1.5,-3*sqrt(3)),N);
label("$y^\circ$",(1.2,-2));
[/asy]

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