
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
A particle moves in a straight line, and its distance from the starting point (in meters) at time $x$ (in seconds) is given by $f(x)= \frac {2}{3}x^{3}+x^{2}+2x$.
1. Find the average velocity of the particle during the first second.
2. Find the instantaneous velocity of the particle at the end of the first second.
3. After how long does the particle's velocity reach $14m/s$?

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