
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 $y=f(x)$, the function corresponding to the graph of $y=f(x)$ symmetric about the $y$-axis is $y=F(x)$. An interval $[a, b]$ is called the "invariant interval" of the function $y=f(x)$ when the function $y=f(x)$ and $y=F(x)$ are both increasing or both decreasing on the interval $[a, b]$. If the interval $[1, 2]$ is the "invariant interval" for the function $y=|2^x - t|$, find the maximum value of the real number $t$.

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