
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 \( f(x) = a \sin x - b \sqrt[3]{x} + c \ln \left(x + \sqrt{x^2 + 1}\right) + 4 \), where \( a, b, c \) are real numbers, and \( f(\lg \log_{3} 10) = 5 \). Find the value of \( f(\lg \lg 3) \).

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