
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 $\triangle ABC$, where $C= \dfrac {\pi}{2},A= \dfrac {\pi}{6}$ and $AB=2$, calculate $\overrightarrow{AB}\cdot \overrightarrow{BC}+ \overrightarrow{BC}\cdot \overrightarrow{CA}+ \overrightarrow{CA}\cdot \overrightarrow{AB}$.

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