
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 an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).

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