
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
For a three-digit positive integer $n$, if $n$ satisfies: the sum of its hundreds digit and tens digit minus the units digit equals $6$, then this number $n$ is called a "happy number". For example: $n_{1}=936$, because $9+3-6=6$, so $936$ is a "happy number"; $n_{2}=602$, because $6+0-2=4\neq 6$, so $602$ is not a "happy number". If we double the units digit of a "happy number" $m$ and place it in the hundreds place, the original hundreds digit becomes the tens digit, and the original tens digit becomes the units digit, resulting in a new three-digit number $s$ (for example; if $m=543$, then $s=654). If $s$ is also a "happy number", then the values of all $m$ that satisfy the conditions are ______.

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