
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 the non-zero vectors $\bar{AB}$ and $\bar{AC}$ satisfy $\left(\frac{\bar{AB}}{|\bar{AB}|} + \frac{\bar{AC}}{|\bar{AC}|}\right) \cdot \bar{BC} = 0$, and $\frac{\bar{AB}}{|\bar{AB}|} \cdot \frac{\bar{AC}}{|\bar{AC}|} = \frac{1}{2}$, determine the type of $\Delta ABC$.

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