
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
Two classes organize a joint club afternoon. To cover the costs, each student from class $A$ contributed $5 \mathrm{Ft}$, and each student from class $B$ contributed $3 \mathrm{Ft}$. If class $A$ students had covered all the costs, it would have cost each of them $K \mathrm{Ft}$. For the second joint event, class $A$ students contributed $4 \mathrm{Ft}$ each, and class $B$ students contributed $6 \mathrm{Ft}$ each, and the total amount of money collected was the same as if each student from class $B$ had paid $K$ \mathrm{Ft}. What is the value of $K$, and which class has more students?

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