
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
If a certain number of chickens are placed into a certain number of cages, if 4 chickens are placed in each cage, there will be one chicken left without a cage; if 5 chickens are placed in each cage, there will be one cage left empty. Let the number of cages be $x$. Please list the inequality that $x$ must satisfy and explain the minimum and maximum number of chickens and cages.

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