
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 $PQR,$ $PQ = 7,$ $QR = 15,$ and $PR = 14.$ If $F$ and $G$ are points on $\overline{PQ}$ and $\overline{PR}$ respectively such that $PF = 2$ and $PG = 5,$ then determine the area of triangle $PFG.$

[asy]
unitsize (1 cm);

pair P, Q, R, F, G;

P = (3,4);
Q = (0,0);
R = (8,0);
F = interp(P,Q,0.5);
G = interp(P,R,4/5);

draw(P--Q--R--cycle);
draw(F--G);

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

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