
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 positive integers $a$ and $b$ be such that the product \[\log_a(a+2) \cdot \log_{a+2}(a+4) \dotsm \log_{b-4}(b-2) \cdot \log_{b-2}b\]
contains exactly $430$ terms, and its value is $3$. Compute $a+b$.

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