
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
Observe the following three rows of numbers and complete the subsequent questions:

①-2, 4, -8, 16, ...
②1, -2, 4, -8, ...
③0, -3, 3, -9, ...

(1) Consider the pattern in row ① and write the expression for the $n^{th}$ number.
(2) Denote the $m^{th}$ number in row ② as $a$ and the $m^{th}$ number in row ③ as $b$. Write the relationship between $a$ and $b$.
(3) Let $x$, $y$, and $z$ represent the $2019^{th}$ number in rows ①, ②, and ③, respectively. Calculate the value of $x + y + z$.

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