
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 \( X \backslash Y = \{a \mid a \in X, a \notin Y\} \) denote the difference of sets \( X \) and \( Y \). Define the symmetric difference of sets \( A \) and \( B \) as \( A \Delta B = (A \backslash B) \cup (B \backslash A) \). Given two non-empty finite sets \( S \) and \( T \) such that \( |S \Delta T| = 1 \), find the minimum value of \( k = |S| + |T| \).

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