
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
It is given that \(\log \frac{x}{2}=0.5\) and \(\log \frac{y}{5}=0.1\). If \(\log xy=c\), find \(c\).

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