
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
What is the area, in square units, of triangle $PQR$?
[asy]
unitsize(0.15inch);
path X = (-6.5, 0)--(7.5, 0);
path Y = (0, -3.5)--(0, 9.5);
draw(X); draw(Y);

for(int n=-6; n <= 7; ++n)
if( n != 0 )
draw( (n,0.25)--(n,-0.25) );
for(int n=-3; n <= 9; ++n)
if( n != 0 )
draw( (0.25,n)--(-0.25,n) );

pair P = (-5,2); pair Q = (1,8); pair R = (5,0);
dot(P); dot(Q); dot(R);
label("$P\ (-5,2)$", P, NW); label("$Q\ (1,8)$", Q, N); label("$R\ (5,0)$", R, SE);
draw(P--Q--R--cycle);
[/asy]

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