
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 a function $f(x)$ defined on $\mathbb{R}$ with its axis of symmetry at $x = -5$, and when $x \geq -5$, $f(x) = 2^x - 3$. If the function $f(x)$ has a zero in the interval $(k, k+1)$ ($k \in \mathbb{Z}$), determine the possible values of $k$.

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