
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
A positive integer is called a perfect power if it can be written in the form \(a^b\), where \(a\) and \(b\) are positive integers with \(b \geq 2\). The increasing sequence \(2, 3, 5, 6, 7, 10, \ldots\) consists of all positive integers which are not perfect powers. Calculate the sum of the squares of the digits of the 1000th number in this sequence.

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