
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 in a sequence \( a_{1}, a_{2}, \cdots, a_{9} \). If \( a_{1}+a_{3}+a_{5}+a_{7}+a_{9} \) is a square number and \( a_{2}+a_{4}+a_{6}+a_{8} \) is a cube number, what is the minimum value of \( a_{1}+a_{2}+\cdots+a_{9} \)?

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