
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 the rectangular coordinate system $xOy$, it is known that point $A$ is on the ellipse $\frac{x^{2}}{25}+ \frac{y^{2}}{9}=1$. Point $P$ satisfies $\overrightarrow{AP}=(λ-1)\overrightarrow{OA}\ (λ∈R)$ and $\overrightarrow{OA}\cdot\overrightarrow{OP}=48$. The maximum length of the projection of line segment $OP$ on the $x$-axis is $\_\_\_\_\_\_$.

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