
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 space vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=1$, $\langle\overrightarrow{a},\overrightarrow{b}\rangle=60^{\circ}$, find the range of real number $\lambda$ for which the angle between the vectors $\overrightarrow{a}+\lambda \overrightarrow{b}$ and $\lambda \overrightarrow{a}-2\overrightarrow{b}$ is obtuse.

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