
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
Let \( a_{1}=1, a_{2}=2 \) and for all \( n \geq 2 \), \[ a_{n+1}=\frac{2 n}{n+1} a_{n}-\frac{n-1}{n+1} a_{n-1}. \] It is known that \( a_{n} > 2 + \frac{2009}{2010} \) for all \( n \geq m \), where \( m \) is a positive integer. Find the least value of \( m \).

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