
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 set  $I=\{(x_1,x_2,x_3,x_4)|x_i\in\{1,2,\cdots,11\}\}$ . $A\subseteq I$ , satisfying that for any  $(x_1,x_2,x_3,x_4),(y_1,y_2,y_3,y_4)\in A$ , there exists  $i,j(1\leq i<j\leq4)$ ,  $(x_i-x_j)(y_i-y_j)<0$ . Find the maximum value of  $|A|$ .

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