
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, $PQR$ is a straight line, and point $T$ is below the line, making triangle $QRT$. What is the value of $x$ if $\angle PQS = 124^\circ$ and $\angle QRT = 76^\circ$? Assume $\angle QRS = x$ and $S$ is a point such that $\triangle QRS$ and $\triangle QRT$ share side $QR$.

[asy]
draw((-2,0)--(8,0),linewidth(0.7)); draw((8,0)--(5,-5.5)--(0,0),linewidth(0.7));
draw((8,0)--(3,-3.8)--(0,0),linewidth(0.7));  // New triangle QRT
label("$P$",(-2,0),W); label("$Q$",(0,0),N); label("$R$",(8,0),E); label("$S$",(5,-5.5),S); label("$T$",(3,-3.8),S);
label("$124^\circ$",(0,0),SW); label("$x^\circ$",(7,0),S);
label("$76^\circ$",(4,-3.8),S);
[/asy]

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