
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
Ancient Hindu mathematicians used the following rational approximation for the number $\sqrt{2}$:

$$
t=1+\frac{1}{3}+\frac{1}{3 \cdot 4}-\frac{1}{3 \cdot 4 \cdot 34}
$$

What is the maximum percentage error of this approximation? How many leading digits do $t$ and the decimal approximation of $\sqrt{2}$ have in common?

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