
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
From the sequence of natural numbers \(1, 2, 3, 4, 5, \cdots\), remove every number that is a multiple of 3 or 4, but keep any number that is a multiple of 5 (for example, 15 and 120 are retained). After performing these steps, the remaining numbers form a new sequence: \(1, 2, 5, 7, 10, \cdots\). Find the 2010th term in this new sequence.

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