
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
Let vectors $\overrightarrow{a}=(-1,3)$ and $\overrightarrow{b}=(2,1)$. If $(\overrightarrow{a}+\lambda \overrightarrow{b}) \perp (\overrightarrow{a}-\lambda \overrightarrow{b})$ and $\lambda > 0$, then the real number $\lambda=$ ______.

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