
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 complex numbers $z_1=2+i$ and $z_2=x-2i$ ($x\in \mathbb{R}$). If $z_1\cdot z_2$ is a real number, then $x$ equals to .

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