
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 poor memory for storing numbers but an excellent memory for remembering sequences of operations. To remember his five-digit bank code, he can recall that:

1. The code has no repeated digits.
2. None of the digits are zero.
3. The first two digits form a power of 5.
4. The last two digits form a power of 2.
5. The middle digit is a multiple of 3.
6. The sum of all the digits is an odd number.

Now he doesn't need to memorize the number because he knows his code is the largest number that satisfies these conditions. What is this code?

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