
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 plane quadrilateral \(ABCD\), points \(E\) and \(F\) are the midpoints of sides \(AD\) and \(BC\) respectively. Given that \(AB = 1\), \(EF = \sqrt{2}\), and \(CD = 3\), and that \(\overrightarrow{AD} \cdot \overrightarrow{BC} = 15\), find \(\overrightarrow{AC} \cdot \overrightarrow{BD}\).

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