
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
A sequence $(a_1,b_1)$, $(a_2,b_2)$, $(a_3,b_3)$, $\dots$ of points in the coordinate plane satisfies
\[(a_{n + 1}, b_{n + 1}) = (2 a_n - b_n, 2 b_n + a_n)\]
for \( n = 1, 2, 3, \ldots \). Suppose that $(a_{50}, b_{50}) = (5, -3)$. Determine $a_1 + b_1$.

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