
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 that $\triangle ABC$ is an equilateral triangle with side length $1$, point $D$ and $E$ are the midpoints of sides $AB$ and $BC$ respectively. Connect $DE$ and extend it to point $F$ such that $DE=2EF$. Calculate the value of $\overrightarrow{AF} \cdot \overrightarrow{BC}$.

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