
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 Peukert formula $C = I^{n} \cdot t$, with constant battery capacity $C$, calculate the value of the Peukert constant $n$ for a storage battery, given that when the discharge current $I = 20A$, the discharge time $t = 20h$, and when the discharge current $I = 50A$, the discharge time $t = 5h$, with $\lg 2 \approx 0.3$ used in the calculation.

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