
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 vectors $|\vec{a}|=1,|\vec{b}|=2$, and the angle between $\vec{a}$ and $\vec{b}$ is $120^{\circ}$. If the angle between $\vec{a}+t \vec{b}$ and $t \vec{a}+\vec{b}$ is acute, then the range of values for $t$ is $\qquad$ .

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