
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 an equilateral triangle \(ABC\) with side length 1, let \(\overrightarrow{BC} = \vec{a}\), \(\overrightarrow{CA} = \vec{b}\), and \(\overrightarrow{AB} = \vec{c}\). Evaluate the expression \(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}\).

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