
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
A function $y = f(x)$ defined on $\mathbb{R}$ is an even function satisfying the following conditions:
1. For any $x \in \mathbb{R}$, the identity $f(x + 2) = f(x) + f(1)$ holds true.
2. $f(0) = -1$.
3. For $x \in (-1, 0)$, the inequality $f'(x) < 0$ is satisfied.
If the equation $f(x) = 0$ has exactly three distinct real roots in the interval $[a, 3]$, then the range of the real number $a$ is _______.

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