
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
The function $y=f(x)$ (where $x \in \mathbb{R}$ and $x > 0$) satisfies the following conditions: (1) $f(2x) = 2f(x)$; (2) when $2 \le x \le 4$, $f(x) = 1 - |x - 3|$. Find the smallest element of the set $S = \{x | f(x) = f(36)\}$.

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