
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 $A=\{1,2, \cdots, 366\}$. If a two-element subset $B=\{a, b\}$ of $A$ satisfies $17 \mid(a+b)$, then $B$ is said to have property $P$.
(1) Find the number of two-element subsets of $A$ that have property $P$.
(2) What is the number of mutually disjoint two-element subsets of $A$ that have property $P$?

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