
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
Solve the equation:

a) \(1 - \lg 5 = \frac{1}{3}\left(\lg \frac{1}{2} + \lg x + \frac{1}{3} \lg 5\right)\);

b) \(\log_{1/3}(-1/x) = 2\);

c) \(\lg (2x - 5)^2 = 0\).

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