
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
As in the following diagram, square  $ABCD$  and square  $CEFG$  are placed side by side (i.e.  $C$  is between  $B$  and  $E$  and  $G$  is between  $C$  and  $D$ ). If  $CE = 14$ ,  $AB > 14$ , compute the minimal area of  $\triangle AEG$ . 
[asy]
size(120); defaultpen(linewidth(0.7)+fontsize(10)); 
pair D2(real x, real y) {
 pair P = (x,y);
 dot(P,linewidth(3)); return P;
}
int big = 30, small = 14;
filldraw((0,big)--(big+small,0)--(big,small)--cycle, rgb(0.9,0.5,0.5));
draw(scale(big)*unitsquare); draw(shift(big,0)*scale(small)*unitsquare);
label(" $A$ ",D2(0,big),NW);
label(" $B$ ",D2(0,0),SW);
label(" $C$ ",D2(big,0),SW);
label(" $D$ ",D2(big,big),N);
label(" $E$ ",D2(big+small,0),SE);
label(" $F$ ",D2(big+small,small),NE);
label(" $G$ ",D2(big,small),NE);
[/asy]

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