
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 \( x \in (-1, 1) \), \( f(x) \) be an even function, and \( g(x) \) be an odd function, and \( f(x) + g(x) = -2 \log_{10} (1 + x) \). Find \( 10^{f(x)} \) and \( 10^{g(x)} \).

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