
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 two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=1$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$. If the angle between the vector $2t\overrightarrow{a}+7\overrightarrow{b}$ and $\overrightarrow{a}+t\overrightarrow{b}$ is obtuse, then the range of the real number $t$ is \_\_\_\_\_\_.

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