
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((-2,-2*sqrt(3))--(3,3*sqrt(3))--(3,-2*sqrt(3))--(-2*sqrt(3)/.9,-2*sqrt(3))--(3,2.7));
draw((2.7,-2*sqrt(3))--(2.7,-2*sqrt(3)+.3)--(3,-2*sqrt(3)+.3));
label("$42^\circ$",(3,1.5),W);
label("$50^\circ$",(-1.2,-2*sqrt(3)),N);
label("$x^\circ$",(1,-1));
[/asy]

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