
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 \( f(x) = a + x - b^x \) has a zero point \( x_0 \in (n, n+1) \) where \( n \in \mathbf{Z} \), and the constants \( a \) and \( b \) satisfy the conditions \( 2019^a = 2020 \) and \( 2020^b = 2019 \), determine the value of \( n \).

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