
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
Let  $A$  be Abelian group of order  $p^4$ , where  $p$  is a prime number, and which has a subgroup  $N$  with order  $p$  such that  $A/N\approx\mathbb{Z}/p^3\mathbb{Z}$ . Find all  $A$  expect isomorphic.

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