
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
A school math club is designing a desert tree planting scheme on graph paper as follows: The \(k\)-th tree is planted at point \(P_{k}(x_{k}, y_{k})\), where \(x_{1}=1\) and \(y_{1}=1\). For \(k \geq 2\), the coordinates are given by the equations:
\[ \left\{\begin{array}{l} x_{k} = x_{k-1} + 1 - 5\left[\frac{k-1}{5}\right] + 5\left[\frac{k-2}{5}\right], \\ y_{k} = y_{k-1} + \left[\frac{k-1}{5}\right] - \left[\frac{k-2}{5}\right]. \end{array}\right. \]

where \([a]\) denotes the integer part of the real number \(a\) (e.g. \([2.6] = 2\) and \([0.6] = 0\)). According to this scheme, what are the coordinates of the 2008th tree planting point?

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