
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
Let \( f(n) = 2n + 1 \) for \( n \in \mathbf{N} \), \( U = \mathbf{N} \), \( P = \{1, 2, 3, 4, 5\} \), \( Q = \{3, 4, 5, 6, 7\} \). Define \( A = \{ n \mid f(n) \in P, n \in \mathbf{N} \} \) and \( B = \{ n \mid f(n) \in Q, n \in \mathbf{N} \} \).
Calculate \( (A \cap \complement_{U} B) \cup (B \cap \complement_{U} A) \).

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