
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 functions $f\left(x\right)=2^{x}$ and $g\left(x\right)=\log _{a}x$, if for any point $P$ on the graph of $f\left(x\right)$, there always exists a point $Q$ on the graph of $g\left(x\right)$ such that $OP\bot OQ$ and $|OP|=|OQ|$, then the real number $a=\_\_\_\_\_\_$.

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