
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 vectors $\overrightarrow{a}=({1,2})$ and $\overrightarrow{b}=({2,1})$, and $({\overrightarrow{a}+\overrightarrow{b}})⊥({\overrightarrow{a}-λ\overrightarrow{b}})$, find the real number $\lambda$.

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