
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 $f(x)=x^{2}-4x+3$ and $g(x)=3^{x}-2$, and the sets $M=\{x\in\mathbb{R}\mid f(g(x)) > 0\}$ and $N=\{x\in\mathbb{R}\mid g(x) < 2\}$, find the intersection $M\cap N$.

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