
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
In an arithmetic sequence, the third term is 14 and the eighteenth term is 23. Determine how many terms in the first 2010 terms of this sequence are integers.

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