
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
The diagram below shows an isosceles triangle with base  $21$  and height  $28$ .  Inscribed in the triangle is a square.  Find the area of the shaded region inside the triangle and outside of the square.

[asy]
size(170);
defaultpen(linewidth(0.8));
draw((0,0)--(1,1));
pair A=(5,0),B=(-5,0),C=(0,14), invis[]={(1,2),(-1,2)};
pair intsquare[]={extension(origin,invis[0],A,C),extension(origin,invis[1],B,C)};
path triangle=A--B--C--cycle,square=(intsquare[0]--intsquare[1]--(intsquare[1].x,0)--(intsquare[0].x,0)--cycle);
fill(triangle,gray);
unfill(square);
draw(triangle^^square);
[/asy]

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