
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 four-digit natural number $m$ where each digit is not zero, if the sum of the thousands and hundreds digits is equal to the sum of the tens and units digits, then $m$ is called a "consistent number." Let a "consistent number" $m=\overline{abcd}$ satisfy $a\leqslant 8$ and $d=1$. Swap the thousands and tens digits of $m$, and swap the hundreds and units digits to get a new number $m'$. Let $F(m)=\frac{m+m'}{101}$; for a two-digit number $N=10a+2b$, let the sum of the digits of $N$ be denoted as $G(N)$; when $F(m)-G(N)-4a=k^{2}+3$ (where $k$ is an integer), then among all the "consistent numbers" $m$ that satisfy the condition, if $G(N)$ is even, the value of $k$ is ______, and the value of $m$ is ______.

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