
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 the sets \( X = \{ -10, -1, 1 \} \) and \( Y = \{ -2, -1, 0, 1, 2 \} \). If the mapping \( f \) from \( X \) to \( Y \) satisfies the condition that for each \( x \in X \), \( x + f(x) \) is an odd number, determine the number of possible mappings.

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