
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
The school's track and field sports day is coming soon. Xiao Gang used his pocket money to buy a pair of sports shoes and wanted to study the relationship between shoe size and foot size. So, when Xiao Gang got home, he measured his mother's size 36 shoes, which were 23cm in length; he measured his father's size 42 shoes, which were 26cm in length; he also measured his newly bought shoes, which were 24.5cm in length; then, he looked at the shoe size of the shoes he bought, but he couldn't understand the relationship between a pair of shoes' size and its inner length. With this question, Xiao Gang went to ask his math teacher, who said: Let the inner length of the shoe be $x$ cm, and the shoe size be $y$, then $y$ is a linear function of $x$. Please write down this linear function and calculate what size shoes Xiao Gang bought?

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