
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
Given three points \(A\), \(B\), and \(C\) in a plane satisfying \(|\overrightarrow{AB}| = 3\), \(|\overrightarrow{BC}| = 4\), and \(|\overrightarrow{CA}| = 5\), determine the value of \(\overrightarrow{AB} \cdot \overrightarrow{BC} + \overrightarrow{BC} \cdot \overrightarrow{CA} + \overrightarrow{CA} \cdot \overrightarrow{AB}\).

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