
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 ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$ ($a>b>0$) with its left and right foci being $F_1$ and $F_2$ respectively, and its eccentricity is $\frac { \sqrt {3}}{3}$. Point $M$ is a point on the ellipse, and the maximum area of triangle $MF_1F_2$ is $\sqrt {2}$.  
(1) Find the standard equation of the ellipse.  
(2) Suppose a line $\ell: y=kx+m$ that does not pass through focus $F_1$ intersects the ellipse at two distinct points $A$ and $B$. If the slopes of lines $AF_1$, $\ell$, $BF_1$ form an arithmetic sequence in order, find the range of values for $m$?

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