
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
Given the right triangles ABC and ABD, what is the length of segment BC, in units? [asy]
size(150);
pair A, B, C, D, X;
A=(0,0);
B=(0,15);
C=(-20,0);
D=(-45,0);
draw(A--B--D--A);
draw(B--C);
draw((0,2)--(-2,2)--(-2,0));
label("$53$", (B+D)/2, NW);
label("$25$", (C+D)/2, S);
label("$20$", (A+C)/2, S);
label("A", A, SE);
label("B", B, NE);
label("D", D, SW);
label("C", C, S);
[/asy]

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