
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 the diagram, $ABCD$ and $EFGD$ are squares each of area 25. $H$ is the midpoint of both $BC$ and $EF$. Another square $IJKL$ intersects $ABCD$ and $EFGD$ such that $D$ is the midpoint of $JK$ and $L$ lies on line $EF$. Find the total area of polygon $ABIJKFGD$.

[asy]
unitsize(3 cm);

pair A, B, C, D, E, F, G, H, I, J, K, L;

D = (1,1);
F = (0,0);
G = (1,0);
E = (0,1);
H = (E + F)/2;
I = (1, -1);
J = (2, -1);
K = (2, 1);
L = (1, 0);

A = (2,2);
B = (1,2);
C = (1,1);

draw(A--B--C--D--cycle);
draw(D--E--F--G--cycle);
draw(I--J--K--L--cycle);

label("$A$", A, N);
label("$B$", B, NW);
label("$C$", C, NE);
label("$D$", D, NE);
label("$E$", E, NW);
label("$F$", F, SW);
label("$G$", G, SE);
label("$H$", H, SW);
label("$I$", I, SW);
label("$J$", J, S);
label("$K$", K, E);
label("$L$", L, S);
[/asy]

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