
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 certain breeder's annual breeding cost includes fixed costs and variable costs, with fixed costs amounting to $40,000 per year, and variable costs increasing each year. It is known that the variable cost in the first year is $26,000. Let the percentage increase in variable costs per year be $x$.  
$(1)$ Express the variable cost in the third year in terms of $x$.  
$(2)$ If the breeder's breeding cost in the third year is $71,460, find the percentage increase $x$ in variable costs per year.

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