
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
Several kilograms of two types of goods are purchased: the first type for 45 rubles and the second type for 20 rubles. The amount of the first type purchased is 1 kg more than the amount of the second type. The price per kilogram of the first type is a rubles more than the price per kilogram of the second type. How many kilograms of each type of goods were purchased? Determine the number of solutions depending on the possible values of \( a \).

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