
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
Before the Mid-Autumn Festival, the school held a series of activities called "Passing on Classics, Celebrating Mid-Autumn Festival", which included four activities: tasting mooncakes, telling stories, reciting poems, and creating beautiful articles. Four cards numbered $A$, $B$, $C$, and $D$ were made to represent each activity (as shown in the table, except for the numbers and content, the rest are exactly the same), and they were shuffled with the backs facing up and placed on the table.

| $A$. Tasting Mooncakes | $B$. Telling Stories | $C$. Reciting Poems | $D$. Creating Beautiful Articles |
|------------------------|----------------------|-------------------|----------------------------------|

$(1)$ Xiaoli randomly draws $1$ card, the probability of drawing the card numbered $A$ is ______;  
$(2)$ Xiaoli randomly draws $1$ card from the $4$ cards (without replacement). Xiaoming then randomly draws $1$ card from the remaining $3$ cards. Find the probability that exactly one of Xiaoli and Xiaoming recites poems (please write out the solution process using "drawing a tree diagram" or "list" methods).

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