
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
Consider two right triangles ABC and ABD, where D is moved to make the length $AD$ longer, such that $AD = 30$ units. All other measurements remain the same as before except $BD$ which needs recalculations as below. Calculate the new length of segment $BC$ in units.
```asy
size(150);
pair A, B, C, D, X;
A = (0, 0);
B = (0, 12);
C = (-16, 0);
D = (-35, 5);
draw(A--B--D--A);
draw(B--C);
draw((0, 1.5)--(-1.5, 1.5)--(-1.5, 0));
label("$16$", (A + C)/2, S);
label("A", A, SE);
label("B", B, NE);
label("C", C, S);
label("D", D, SW);
```

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