
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 $\overrightarrow {b}$, where $| \overrightarrow {a}|=2$ and $| \overrightarrow {b}|=1$:

1. If $( \overrightarrow {a}+2 \overrightarrow {b})\cdot ( \overrightarrow {a}- \overrightarrow {b})=1$, find the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$.
2. If the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is 60°, and the angle between vectors $2t \overrightarrow {a}+7 \overrightarrow {b}$ and $\overrightarrow {a}+t \overrightarrow {b}$ is obtuse, find the range of real number $t$.

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