
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 \( a_{i} > 0 \) for \( i = 1, 2, \ldots, 2020 \) and \( \sum_{i=1}^{2020} a_{i} = 2020 \), find the maximum value of \( \sum_{k=1}^{2020} a_{k}^{\frac{1}{k^{2}}} \).

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