
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 $f(x) = ah(x) + bg(x) + 4$, where $h(x)$, $g(x)$ are odd functions, and $a$, $b$ are constants that are not both zero. If $f[\lg(\log_{3}{10})] = 5$, determine the value of $f[\lg(\lg{3})]$.

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