
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 $g_0(x) = 2x + |x-150| - |x+150|$, and define $g_n(x) = |g_{n-1}(x)| - 3$ for each $n \ge 1$. Determine the number of values of $x$ for which $g_{50}(x) = 0$.

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