
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
On the interval $[-3,3]$, consider the function $f(x)$ given by a piecewise linear graph with endpoints connected as $(-3, -3)$ to $(-2, -3)$, $(-2, -2)$ to $(-1, -2)$, $(-1, -1)$ to $(0, -1)$, $(0, 0)$ to $(1, 0)$, $(1, 1)$ to $(2, 1)$, and $(2, 2)$ to $(3, 2)$. Find the range of the expression $f(x) + x$ over this interval. Express your answer in interval notation.

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