
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
A children's clothing factory currently has 38 meters of Type A fabric and 26 meters of Type B fabric. It plans to use these two types of fabrics to produce a total of 50 sets of children's clothing in sizes L and M. It is known that making one set of size L clothing requires 0.5 meters of Type A fabric and 1 meter of Type B fabric, yielding a profit of 45 yuan; making one set of size M clothing requires 0.9 meters of Type A fabric and 0.2 meters of Type B fabric, yielding a profit of 30 yuan. Let the number of sets of size L clothing produced be $x$, and the profit from producing these two sizes of clothing with this batch of fabric be $y$ (in yuan); write the function expression of $y$ (in yuan) in terms of $x$ (in sets), and the range of values for the independent variable $x$.

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