
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
Define a function $f(x)$ on $\mathbb{R}$ whose graph passes through points $M(-6, 2)$ and $N(2, -6)$, and for any positive real number $k$, it holds that $f(x+k) < f(x)$. When the solution set of the inequality $|f(x-t) + 2| < 4$ is $(-4, 4)$, the value of the real number $t$ is ____.

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