
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
In the function $f(x) = ax^3 + b\sin x + 4$ (where $a, b \in \mathbb{R}$), it is given that $f(\lg(\log_2{10})) = 5$. Find the value of $f(\lg(\lg{2}))$.

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