
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
Consider two ellipses ($C_1$ and $C_2$) with foci on the $x$-axis, described by the equations $C_1: \frac{x^2}{4} + \frac{y^2}{3} = 1$ and $C_2: \frac{x^2}{9} + \frac{y^2}{m} = 1$. If $C_1$ is flatter than $C_2$, find the range of possible values for $m$.

A) $\left( \frac{27}{4}, +\infty \right)$
B) $\left( \frac{3\sqrt{3}}{2}, +\infty \right)$
C) $\left( \frac{27}{4}, 9 \right)$
D) $\left( \frac{3\sqrt{3}}{2}, 9 \right)$

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