
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
Consider a geometric progression of six terms, each a positive integer less than $150$. The sum of the six terms is $450$. If $P$ is the product of those terms in the progression which are cubes of integers, find the value of $P$.
A) 90
B) 160
C) 280
D) 450

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