
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  $X={1,2,3,4,5,6,7,8,9,10}$  and  $A={1,2,3,4}$ . Find the number of  $4$ -element subsets  $Y$  of  $X$  such that  $10\in Y$  and the intersection of  $Y$  and  $A$  is not empty.

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