
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 that on the number line, points $A$ and $B$ represent the numbers $a$ and $b$ respectively, $|a-1|=5$, $b^{3}=-27$, $|a-b|=a-b$, point $P$ lies on the number line and $PA=2PB$, then the number represented by point $P$ is ______.

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