
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
I am thinking of a four-digit number, where each digit is different. When I omit the last two digits of this number, I get a prime number. Similarly, I get a prime number if I omit the second and fourth digits, and also if I omit the middle two digits. However, the number I am thinking of is not a prime number itself - it can be divided by three without a remainder. There are several numbers with these properties, but mine is the largest of them. Which number am I thinking of?

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