
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 sets $M = \{3, \log_{2}4\}$, $N = \{x, y\}$, and $M \cap N = \{2\}$, the function $f: M \rightarrow N$ satisfies: for any $x \in M$, $x + f(x)$ is an odd number. Determine the number of functions $f$ that meet the condition.

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