
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

Esquecinaldo has a terrible memory for numbers but a great one for remembering sequences of operations. To remember his 5-digit bank code, he recalls that:
- None of the digits are zero.
- The first two digits form a power of 5.
- The last two digits form a power of 2.
- The middle digit is a multiple of 3.
- The sum of all the digits is an odd number.
He also knows that the number is the largest number that meets these conditions and does not have repeated digits. What is this code?

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