
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
Let \( f(x) = ax + b \), where \( a \) and \( b \) are real numbers, \( f_1(x) = f(x), \) \( f_{n+1}(x) = f(f_n(x)), \) for \( n = 1, 2, 3, \ldots \). If \( f_7(x) = 128x + 381 \), find \( a + b = \quad \).

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