
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
Nine consecutive positive integers are arranged in ascending order to form a sequence \( a_{1}, a_{2}, \cdots, a_{9} \). If the value of \( a_{1} + a_{3} + a_{5} + a_{7} + a_{9} \) is a perfect square, and the value of \( a_{2} + a_{4} + a_{6} + a_{8} \) is a perfect cube, what is the minimum value of the sum of these nine positive integers?

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