
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
Given the sequences $\{a_{n}\}$ and $\{b_{n}\}$ that satisfy $a_{1}=2$, $b_{1}=0$, $2a_{n+1}=3a_{n}+b_{n}+2$, and $2b_{n+1}=a_{n}+3b_{n}-2$, find the value of $a_{2024}+b_{2023}$.

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