
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 high school mathematics, it is common to generalize from specific cases and abstract from concrete instances. For example, from $f(x) = \lg(x)$, we can abstract the property that $f = f(x_1) + f(x_2)$. Given this, if we have $h(x) = $ (fill in a specific function), we can abstract the property $h(x_1 + x_2) = h(x_1) \cdot h(x_2)$.

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