
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
(1) Given a set of data $(51,54,m,57,53)$ with an average of $54$, find the standard deviation of the data.

(2) A unit has $624$ on-duty workers. To survey the time workers spend commuting, they decide to use systematic sampling to select $10\%$ of the workers. After randomly removing $4$ people from the total population, the remaining $620$ employees are numbered $(000,001,002,...,619)$. If the smallest number in the sample is $007$, find the largest number in the sample.

(3) In the observation array $(1,1,1),(3,2,6),(5,4,20),(7,8,56),(a,b,c),...$, find $a+b+c$.

(4) $f(x)$ is an even function. When $x \leq 0$, $f(x)=\frac{1}{e} \cdot \frac{1}{e^{x}}-x$. Find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,2)$.

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