
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 \( f(x) \) and \( g(x) \) as defined in Theorem 1, if \( T_1 = 1 \) and \( T_2 = \frac{1}{m} \) (with \( m \in \mathbb{N} \) and \( m > 1 \)), then the smallest positive period of the function \( h(x) = f(x) + g(x) \) is \( \frac{1}{k} \), where \( k = 1 \) or \( k \in \mathbb{N} \), \( k \) is not a multiple of \( m \), and \( m \) is not a multiple of \( k \).

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