
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
Given the functions $f(x)=kx^{2}+(2k-1)x+k$ and $g(x)=\log _{2}(x+k)$, where $k\in R$:
1. If $f(0)=7$, find the minimum value $m$ of function $g(x)$ on the interval $[9,+\infty)$.
2. If $0 < g(1)\leqslant 5$, and the minimum value of function $f(x)$ on the interval $[0,2]$ is not less than $m$ found in part 1, find the range of $k$.

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