
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
A function $g$ is defined with the properties that $g(4x) = 4g(x)$ for all positive real values of $x$, and $g(x) = 2 - |x-5|$ for $3 \leq x \leq 7$. Find the smallest $x$ for which $g(x) = g(5012)$.

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