
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
(The full score of this question is 12 points)  
Given the equation about $x$: $9^x + m \cdot 3^x + 6 = 0$ (where $m \in \mathbb{R}$).  
(1) If $m = -5$, solve the equation;  
(2) If the equation has no real roots, find the range of real numbers $m$.

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