
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
Square $BCFE$ is inscribed in right triangle $AGD$, as shown below. If $AB = 20$ units and $CD = 70$ units, what is the area of square $BCFE$?

\
(draw)
```
draw((9,15.6)--(10.7,14.6)--(11.7,16.3));
draw((0,0)--(10,17.3)--(50,0)--cycle);
draw((7,0)--(25,0)--(25,18)--(7,18)--cycle);
label("$A$",(0,0),SW);
label("$B$",(7,0),S);
label("$C$",(25,0),S);
label("$D$",(50,0),SE);
label("$E$",(7,18),NW);
label("$F$",(25,18),NE);
label("$G$",(10,17.3),N);
```
\

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