
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 a plane point set 
$$
G_{n}=\{(i, j) \mid i=1,2, \cdots, n ; j=1,2, \cdots, n\} ,
$$
it is known that $G_{2}$ can be covered by 1 triangle and $G_{3}$ can be covered by 2 triangles. How many triangles are needed to cover $G_{2008}$ at minimum?

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