
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 that the graph of the function $f(x) = kx + b$ intersects with the graph of the function $g(x) = 2^x + 1$ at two points $M(x\_1, 2)$ and $N(x\_2, 4)$, determine the solution set of the inequality ${f^{-1}}(x) \geqslant {g^{-1}}(x)$.

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