
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
The digits of the three-digit integers  $a, b,$  and  $c$  are the nine nonzero digits  $1,2,3,\cdots 9$  each of them appearing exactly once. Given that the ratio  $a:b:c$  is  $1:3:5$ , determine  $a, b,$  and  $c$ .

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