
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]


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Given the half-life of $^{14}C$ is $5730$ years, and it decays at a rate such that $\lg 2$ times the decay constant is approximately $3.3219$, determine the real number value of the approximate age $m$ of the ancient object, knowing that its $^{14}C$ content is $\frac{1}{5}$ of the original amount.

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