
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
As the summer vacation approaches, a fitness club launches a summer promotion for students. The details of the promotion are as follows:<br/>Plan 1: Purchase a $80$ yuan student summer exclusive card, with a fitness fee of $10$ yuan each time;<br/>Plan 2: Without purchasing the student summer exclusive card, the fitness fee is $20$ yuan each time.<br/>$(1)$ Let the number of fitness sessions be $x$ (times) and the total cost be $y$ (yuan). Write down the function expression of $y$ in terms of $x$ for both plans;<br/>$(2)$ In what range of number of sessions is it more cost-effective to choose Plan 1?

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