
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
If a binary number $n=\left(a_{m} a_{m-1} \cdots a_{1} a_{0}\right)_{2}$ satisfies $\left(a_{m} a_{m-1} \cdots a_{1} a_{0}\right)_{2}=$ $\left(a_{0} a_{1} \cdots a_{m-1} a_{m}\right)_{2}$, then $n$ is called a "binary palindrome." How many "binary palindrome" numbers are there among the natural numbers not exceeding 1988?

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