
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 points $O(0,0)$, $A(1,0)$, and $B(0,1)$, point $P$ is a moving point on line segment $AB$ such that $\overrightarrow{A P}=\lambda \overrightarrow{A B}$. If $\overrightarrow{O P} \cdot \overrightarrow{A B} \geq \overrightarrow{P A} \cdot \overrightarrow{P B}$, find the range of the real number $\lambda$.

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