
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
If $a$ belongs to positive real numbers $R^{+}$, then when the minimum value of $a+ \frac{1}{9a}$ is $m$, the solution set of the inequality $m^{x^{2}+4x+3} < 1$ is _______ .

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