
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
The variable \(a\) can take the following values: \(-32, -30, -28, \ldots, 2, 4, 6, 8\), and the variable \(b\) can take the following values: \(-17, -15, -13, \ldots, 11, 13\). How many different values can the expression \(a + b\) take? Find the product of the largest and smallest values of the expression \(a + b\).

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