
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
Point \( F \) is taken on the extension of side \( AD \) of parallelogram \( ABCD \). \( BF \) intersects diagonal \( AC \) at \( E \) and side \( DC \) at \( G \). If \( EF = 18 \) and \( GF = 27 \), then find \( BE \).
[asy]
size(7cm);
pair A = (0, 0), B = (7, 0), C = (10, 5), D = (3, 5), F = (5.7, 9.5);
pair G = intersectionpoints(B--F, D--C)[0];
pair E = intersectionpoints(A--C, B--F)[0];
draw(A--D--C--B--cycle);
draw(A--C);
draw(D--F--B);
label("$A$", A, SW);
label("$B$", B, SE);
label("$C$", C, NE);
label("$D$", D, NW);
label("$F$", F, N);
label("$G$", G, NE);
label("$E$", E, SE);
//Credit to MSTang for the asymptote
[/asy]

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