
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 $x?$ 
[asy]
draw(Arc((0,0),1,-120,42));

draw((-3,-3*sqrt(3))--(4,4*sqrt(3))--(4,-3*sqrt(3))--(-3*sqrt(3)/.9,-3*sqrt(3))--(4,3.6));
draw((3.6,-3*sqrt(3))--(3.6,-3*sqrt(3)+.3)--(4,-3*sqrt(3)+.3));
label("$72^\circ$",(4,2),W);
label("$45^\circ$",(-1.8,-3*sqrt(3)),N);
label("$x^\circ$",(1,-1.5));
[/asy]

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