
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 sequence \( a_{1}, a_{2}, a_{3}, \ldots \) is an arithmetic sequence with common difference 3 and \( a_{1}=1 \). The sequence \( b_{1}, b_{2}, b_{3}, \ldots \) is an arithmetic sequence with common difference 10 and \( b_{1}=2 \). What is the smallest integer larger than 2023 that appears in both sequences?

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