
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
Let $a, b,$ and $c$ be three non-zero integers such that $a + b + c = 30$ and \[\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{450}{abc} = 1.\] Find the value of $abc$.

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