
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 parallelogram $ABCD$, $\overrightarrow{AE} = \overrightarrow{EB}$, $\overrightarrow{CF} = 2\overrightarrow{FB}$, lines $CE$ and $DF$ intersect at point $M$. If $\overrightarrow{AM} = \lambda \overrightarrow{AB} + \mu \overrightarrow{AD}$, then the product of $\lambda$ and $\mu$ is \_\_\_\_\_\_.

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