
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 that the half-life of $^{14}C$ is 5730 years (which means that after 5730 years, the remaining amount of $^{14}C$ is half of the original amount), let the original amount of $^{14}C$ be $a$, and the remaining amount after $x$ years be $b$. The relationship between the remaining amount $b$ and the original amount $a$ is as follows: $b=ae^{-kx}$, where $x$ represents the elapsed time, and $k$ is a constant. It is now measured that the remaining amount of $^{14}C$ in the female corpse of the Mawangdui Han Tomb in Hunan Province is approximately 76.7% of the original amount. Please infer the approximate age of the Mawangdui Han Tomb, which is about \_\_\_\_\_\_ years ago. (It is known that $\log_2 0.767 \approx -0.4$)

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