
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 graph of $y = f(x)$, where $f(x)$ is the quadratic function $f(x) = \frac{x^2}{4} - x - 1$, compute the sum of all distinct $x$ such that $f(f(f(x))) = 1$. Assume $f(x)$ is graphed on an axis with a distance between grid lines equal to $1$ unit.

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