
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]


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The discrete independent random variables \(X\) and \(Y\) are given by the distributions:

![](https://cdn.mathpix.com/cropped/2024_05_22_1d1b16277022f98e68adg-134.jpg?height=105&width=666&top_left_y=482&top_left_x=276)

Find the distribution of the random variable \(Z = X + Y\).

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