
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 math extracurricular activity group at a certain school designed a tree planting plan on graph paper for a desert 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 determined by:

\[
\begin{cases}
x_{k} = x_{k-1} + 1 - 5 \left[\frac{k-1}{5}\right] + 5 \left[\frac{k-2}{5}\right], \\
y_{k} = y_{k-1} + \left[\frac{k-1}{5}\right] - \left[\frac{k-2}{5}\right],
\end{cases}
\]

where $[a]$ denotes the integer part of the real number $a$, for example, $[2.6] = 2$ and $[0.6] = 0$. According to this plan, the coordinates of the 2008th tree are _____

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