
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 five different physics problems numbered $1$, $2$, $3$, $4$, $5$ and four different chemistry problems numbered $6$, $7$, $8$, $9$. Student A randomly selects two problems from these nine, with each problem having an equal chance of being selected. Use the symbol $(x,y)$ to represent the event "the numbers of the two selected problems are $x$ and $y$ respectively, and $x<y$".
(1) How many basic events are there in total? List them.
(2) Calculate the probability that the sum of the numbers of the two problems selected by student A is less than $17$ but not less than $11$.

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