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

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