
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
In the Cartesian coordinate plane xOy, point A(5,0) is given. For a certain positive real number k, there exists a function f(x)=ax^2 with a>0, such that ∠QOA=2∠POA, where P(1, f(1)) and Q(k, f(k)). Determine the range of values for k.

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