
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 \( s \) and \( t \) be two non-zero real numbers, and \( \vec{a} \) and \( \vec{b} \) be unit vectors. Given that the magnitudes of \( s \vec{a} + t \vec{b} \) and \( t \vec{a} - s \vec{b} \) are equal, find the angle between vectors \( \vec{a} \) and \( \vec{b} \).

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