
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
Let  $A$ ,  $B$ ,  $C$ ,  $D$  be four points on a line in this order.  Suppose that  $AC = 25$ ,  $BD = 40$ , and  $AD = 57$ . Compute  $AB \cdot CD + AD \cdot BC$ .

*Proposed by Evan Chen*

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