
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 $\vec{a}$, $\vec{b}$, $\vec{c}$ satisfy $|\vec{a}|=|\vec{b}|=|\vec{c}|\neq 0$, and $\vec{a}+\vec{b}= \sqrt{3} \vec{c}$, then the angle between vector $\vec{a}$ and vector $\vec{c}$ is.

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