
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 $2$, points $D$ and $E$ are on sides $BC$ and $CA$, respectively, and it satisfies $\overrightarrow{DB} + \overrightarrow{DC} = \overrightarrow{O}$, $\overrightarrow{AE} = \frac{1}{2} \overrightarrow{EC}$. Calculate the dot product $\overrightarrow{DA} \cdot \overrightarrow{BE}$.

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