
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 triangle $PQR$, where $PQ = 10$, $QR = 12$, and $PR = 13$. Points $S$ and $T$ are chosen on $\overline{PQ}$ and $\overline{PR}$ such that $PS = 5$ and $PT = 8$. Determine the area of triangle $PST$.
[asy]
unitsize (1 cm);

pair P, Q, R, S, T;

P = (2,3);
Q = (0,0);
R = (6,0);
S = interp(P,Q,0.5);
T = interp(P,R,8/13);

draw(P--Q--R--cycle);
draw(S--T);

label("$P$", P, N);
label("$Q$", Q, SW);
label("$R$", R, SE);
label("$S$", S, NW);
label("$T$", T, NE);
[/asy]

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