
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
There are 48 pencils. If each person in Group A receives 3 pencils, there are pencils left over; if each person receives 4 pencils, there are not enough to go around. In Group B, if each person receives 4 pencils, there are pencils left over; if each person receives 5 pencils, there are not enough to go around. Let Group A have x people and Group B have y people. Then x and y must satisfy the system of inequalities \_\_\_\_\_\_.

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