
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
Let the set \( A = \{1, 2, 3, \ldots, 366\} \). A two-element subset \( B = \{a, b\} \) of \( A \) is said to have property \( P \) if \( 17 \mid (a + b) \).

(1) Find the number of two-element subsets of \( A \) that have property \( P \);

(2) Find the maximum number of pairwise disjoint two-element subsets of \( A \) that have property \( P \).

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