
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
There are 10 different points \( P_{1}(x_{1}, y_{1}), P_{2}(x_{2}, y_{2}), \cdots, P_{10}(x_{10}, y_{10}) \) in the Cartesian plane. If \( x_{i}=x_{j} \) or \( y_{i}=y_{j} \), then \( P_{i} \) and \( P_{j} \) are called a "same-coordinate pair" (the order of \( P_{i} \) and \( P_{j} \) does not matter). It is known that among these 10 different points, the number of "same-coordinate pairs" that each point forms does not exceed \( m \); moreover, it is always possible to partition these points exactly into 5 pairs, where each pair is not a "same-coordinate pair." Find the maximum value of \( m \).

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