
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 magnitude of vector $\overrightarrow{a}$ is $\sqrt {2}$, the magnitude of vector $\overrightarrow{b}$ is 1, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $45^{\circ}$, find the range of real numbers $\lambda$ such that the angle between the vectors $(2 \overrightarrow{a}-λ \overrightarrow{b})$ and $(λ \overrightarrow{a}-3 \overrightarrow{b})$ is acute.

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