
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
In right triangle $\triangle ABC$, $\angle B=90^\circ$, $AB=BC=3$, if $\overrightarrow {BD}$$=2 $$\overrightarrow {DC}$, point $M$ is the midpoint of line segment $AD$, then the value of $\overrightarrow {AM}$$\cdot \overrightarrow {BC}$ is $\_\_\_\_\_\_$.

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