
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
In the diagram, $\triangle ABC$ is right-angled at $A,$ with $AB = 40$ and $AC = 90.$ The point $D$ is on $BC$ so that $AD$ is perpendicular to $BC.$ Determine the length of $BD.$
```
+ Diagram sketch:
pair A, B, C, D;
B = (0, 0);
A = (0, 60);
C = (80, 0);
D = (0, 0);
draw(A--B--C--A--D);
label("B", B, SW);
label("A", A, N);
label("D", D, S);
label("C", C, SE);
label("40", (A+B)/2, W);
label("90", (A+C)/2, NE);
```

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