
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
Given that $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$, where $a, b \in \mathbb{R}$, calculate the result of $(\lg 2)^{3}+3\lg 2\cdot\lg 5+(\lg 5)^{3}+ \frac {1}{2}$ .

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