
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 an investment of $a$ billion yuan is made in infrastructure construction, the social and economic benefits generated after $t$ years are given by the function $f\left(t\right)=ae^{\lambda t}$ billion yuan. If the social and economic benefits generated by investing in infrastructure construction after $4$ years are twice the investment amount, and after another $t_{1}$ years, the social and economic benefits generated by this investment are sixteen times the investment amount, determine the value of $t_{1}$.

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