
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 $\overrightarrow{{e}_{1}}$ and $\overrightarrow{{e}_{2}}$ are two mutually perpendicular unit vectors, if the angle between the vector $\overrightarrow{a}=t\cdot \overrightarrow{{e}_{1}}+\overrightarrow{{e}_{2}}$ and the vector $\overrightarrow{b}=\overrightarrow{{e}_{1}}+t\cdot \overrightarrow{{e}_{2}}$ is obtuse, then the range of the real number $t$ is ______.

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