
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
Divide a line segment into two parts, such that the ratio of one part to the whole length is equal to the ratio of the other part to this part, and the ratio is an irrational number $\frac{\sqrt{5}-1}{2}$. In triangle $\triangle ABC$, point $D$ is the golden section point of line segment $BC$ $(BD > DC)$, $AB=2$, $AC=3$, $\angle BAC=60^{\circ}$, find $\overrightarrow{AD}\cdot \overrightarrow{BC}$.

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