
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
Determine the ionic strength of the solution:

$$
\mu = \frac{1}{2} \left(2^2 \cdot 0.005 + 2^2 \cdot 0.005 + 3^2 \cdot 0.01 + 1^2 \cdot 0.01 \cdot 3\right) = \frac{1}{2} \left(0.02 + 0.02 + 0.09 + 0.03\right) = \frac{1}{2} \cdot 0.16 = 0.08.
$$

Verify the calculated value of $\mu$ using the conjugate method:

$$
\mu = 4c \mathrm{ZnSO}_4 = 4 \cdot 0.005 + 6 \cdot 0.01 = 0.08
$$

For dilute solutions, the activity coefficient can be calculated using the formulas:

$$
\begin{gathered}
\lg f = -0.5 \cdot Z^2 \sqrt{\mu} \text{ for } \mu \leq 0.01 \\
\lg f = -0.5 \cdot Z^2 \sqrt{\mu} /(1 + \sqrt{\mu}) \text{ for } \mu \leq 0.1.
\end{gathered}
$$

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