
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
If a number is randomly selected from the set $\left\{ \frac{1}{3}, \frac{1}{4}, 3, 4 \right\}$ and denoted as $a$, and another number is randomly selected from the set $\{-1, 1, -2, 2\}$ and denoted as $b$, then the probability that the graph of the function $f(x) = a^x + b$ ($a > 0$, $a \neq 1$) passes through the third quadrant is \_\_\_\_\_\_.

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