
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
Triangle  $ABC$  is equilateral.  Points  $D$  and  $E$  are the midpoints of segments  $BC$  and  $AC$  respectively.   $F$  is the point on segment  $AB$  such that  $2BF=AF$ .  Let  $P$  denote the intersection of  $AD$  and  $EF$ ,  The value of  $EP/PF$  can be expressed as  $m/n$  where  $m$  and  $n$  are relatively prime positive integers.  Find  $m+n$ .

[asy]
import olympiad;
size(150);
defaultpen(linewidth(0.7) + fontsize(11pt));
pair A = origin, B = (1,0), C = dir(60), D = (B+C)/2, E = C/2, F = 2*B/3, P = intersectionpoint(A--D,E--F);
draw(A--B--C--A--D^^E--F);
label(" $A$ ",A,SW);
label(" $B$ ",B,SE);
label(" $C$ ",C,N);
label(" $D$ ",D,NE);
label(" $E$ ",E,NW);
label(" $F$ ",F,S);
label(" $P$ ",P,N);
[/asy]

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