
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 the expression:
$$
10 \cdot 73 \log _{3}\left[(3+1)\left(3^{2}+1\right)\left(3^{4}+1\right) \cdots\left(3^{64}+1\right)+\frac{1}{2}\right]+\log _{3} 2
$$
Determine its value.

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