
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
Find all three digit natural numbers of the form  $(abc)_{10}$  such that  $(abc)_{10}$ ,  $(bca)_{10}$  and  $(cab)_{10}$  are in geometric progression. (Here  $(abc)_{10}$  is representation in base  $10$ .)

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