
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
Two perpendicular chords are drawn through a given interior point  $P$  of a circle with radius  $R.$  Determine, with proof, the maximum and the minimum of the sum of the lengths of these two chords if the distance from  $P$  to the center of the circle is  $kR.$ 

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