
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 \( f(x)=\left\{\begin{array}{l}|x|, x \leqslant a, \\ x^{2}-4a x+2a, x > a \end{array}\right. \), if there exists a real number \( m \) such that the equation \( f(x) = m \) has four distinct real roots, determine the range of values for \( a \).

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