
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 the function $f(x)$ satisfies: (1) For any $x \in (0, +\infty)$, it always holds that $f(2x) = 2f(x)$; (2) When $x \in (1, 2]$, $f(x) = 2 - x$. If $f(a) = f(2012)$, then the smallest positive real number $a$ that satisfies the conditions is __________.

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