
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
Pentagon PQRST has a vertical line of symmetry. What is the $y$-coordinate of vertex Q so that the area of the pentagon is 50 square units?
[asy] 
unitsize(2mm); 
defaultpen(linewidth(.7pt)+fontsize(8pt)); 
dotfactor=4;

pair P=(0,0), R=(0,5), Q=(3,18), S=(6,5), T=(6,0); 
pair[] dots={P,R,Q,S,T};

draw(R--Q--S--T); 
dot(dots);

axes(Arrows(4));

label("P(0,0)",P,SW); 
label("T(6,0)",T,SE); 
label("S(6,5)",S,NE); 
label("Q",Q,NE); 
label("R(0,5)",R,NW);
[/asy]

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