
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
Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $15\sqrt{2}$, and $\angle BAC = 30^\circ$. Point $D$ is $25$ meters due north of point $C$. The distance $AD$ is between which two integers?
A) 43 and 44
B) 44 and 45
C) 45 and 46
D) 46 and 47

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