
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
Let non-zero vectors \\(a\\) and \\(b\\) have an angle \\(\theta\\) between them, and define \\(f(a,b)=a\cos \theta-b\sin \theta.\\) If \\(e_{1}\\) and \\(e_{2}\\) are both unit vectors, and \\(e_{1}\cdot e_{2}= \frac{\sqrt{3}}{2}\\), then the angle between vectors \\(f(e_{1},e_{2})\\) and \\(f(e_{2},-e_{1})\\) is ______.

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