
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 triangle $\triangle ABC$, it is known that $AB=6$, $AC=BC=4$. $P$ is the intersection point of the angle bisector of $\angle ACB$ with side $AB$, and $M$ is a point on $PC$ such that $\overrightarrow {BM} = \overrightarrow {BA} + \lambda \left( \frac { \overrightarrow {AC}}{| \overrightarrow {AC}|} + \frac { \overrightarrow {AP}}{| \overrightarrow {AP}|} \right)$ ($\lambda > 0$). Calculate the value of $\frac { \overrightarrow {BM} \cdot \overrightarrow {BA}}{| \overrightarrow {BA}|}$.

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