
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 in the plane $\overrightarrow{a}=\left(1,-2\right)$ and $\overrightarrow{b}=\left(-1,-1\right)$.
1. Find the value of $|2\overrightarrow{a}-\overrightarrow{b}|$.
2. If the angle between the vectors $\overrightarrow{a}+\lambda \overrightarrow{b}$ and $2\overrightarrow{a}-\overrightarrow{b}$ is $\frac{π}{4}$, find the value of the real number $\lambda$.

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