
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]


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Given a function $f(x)$ that satisfies: (1) For any positive real number $x$, it always holds that $f(2x) = 2f(x)$; (2) When $x \in (1, 2)$, $f(x) = 2 - x$. If $f(a) = f(2020)$, determine the smallest positive real number $a$.

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