
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 in the right-angled trapezoid $ABCD$, where $AB\parallel CD$, $AB\perpendicular AD$, $AB=AD=2$, $CD=1$, and $P$ is a moving point on line segment $BC$, let $\overrightarrow {BP}=λ \overrightarrow {BC}$, find the value of $\lambda$ when $\overrightarrow {PA}\cdot \overrightarrow {PD}$ takes the minimum value.

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