
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 an ellipse  $ D: \frac {x^2}{a^2} \plus{} \frac {y^2}{b^2} \equal{} 1\ (a > 0,\ b > 0)$  which contains a circle  $ C: x^2 \plus{} y^2 \equal{} 1.$  Draw a tangent line from the point  $ P(0,\ b)$  on  $ D$ , let the extented line meets  $ D$  at  $ Q$ . Draw a tangent line from  $ Q$ , let the extended line meets  $ D$  at  $ R$ , draw a tangent line from  $ R$ , let the extended line meets  $ D$  at  $ P$ . Express  $ a$  as the function of  $ b$ .

Please translate the context into plain English.

Thanks in advance

kunny

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