
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
A positive integer is a *palindrome* if it is written identically forwards and backwards. For example,  $285582$  is a palindrome. A six digit number  $ABCDEF$ , where  $A, B, C, D, E, F$  are digits, is called *cozy* if  $AB$  divides  $CD$  and  $CD$  divides  $EF$ . For example,  $164896$  is cozy. Determine all cozy palindromes.


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