
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 new diagram, $PQ$ is a line segment. What is the value of $y$?

[asy]
draw((0,0)--(12,0),black+linewidth(1));
draw((5,0)--(5,10),black+linewidth(1));
draw((5,0)--(3.5,0)--(3.5,0.5)--(5,0.5)--cycle,black+linewidth(1));
draw((5,0)--(11,9),black+linewidth(1));
label("$P$",(0,0),W);
label("$Q$",(12,0),E);
label("$y^\circ$",(5.75,3));
label("$68^\circ$",(6.5,1));
label("$F$",(5,0),S);
label("$G$",(5,10),N);
label("$H$",(11,9),NE);
[/asy]

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