
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 the function $f(x) = a^x + x - b$, where its root $x_0 \in (n, n+1) (n \in \mathbb{Z})$, and the constants $a, b$ satisfy $2^a = 3, 3^b = 2$, determine the value of $n$.

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