
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 function 
\[ f(x)=\begin{cases} 
2^{2-x}, & x<2, \\
\log_{3}(x+1), & x \geq 2,
\end{cases} \]
if the equation \( f(x)=m \) has two distinct real roots, then the range of real number \( m \) is (express in interval notation).

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