
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's mathematics extracurricular group has designed a tree-planting plan on graph paper for a vacant lot at the school. The k-th tree is planted at point $P_k(x_k, y_k)$, where $x_1=1$, $y_1=1$. For $k \geq 2$, the coordinates are given by 
$$
\begin{cases}
x_k = x_{k-1} + 1 - 5 \cdot \left[ T\left( \frac{k-1}{5} \right) - T\left( \frac{k-2}{5} \right) \right] \\
y_k = y_{k-1} + T\left( \frac{k-1}{5} \right) - T\left( \frac{k-2}{5} \right)
\end{cases}
$$,
where $T(a)$ denotes the integer part of the non-negative real number $a$ (for example, $T(2.6)=2$, $T(0.2)=0$). According to this plan, the coordinates of the 6th tree planting point should be \_\_\_\_, and the coordinates of the 2016th tree planting point should be \_\_\_\_.

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