
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
A new definition: $\left[a,b,c\right]$ represents the "graph number" of a quadratic function $y=ax^{2}+bx+c$ (where $a\neq 0$, and $a$, $b$, $c$ are real numbers). For example, the "graph number" of $y=x^{2}-2x+3$ is $\left[1,-2,3\right]$. If the "graph number" of the quadratic function is $\left[m,2m+4,2m+4\right]$, and the graph intersects the $x$-axis at only one point, then the value of $m$ is ______.

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