
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 $P$ is a non-empty subset of the set $\{1,2,3,…,2k-1\}$ ($k\in\mathbb{N}^*$, $k\geqslant 2$), and when $x\in P$, it holds that $2k-x\in P$. Let the number of sets $P$ that satisfy the condition be denoted as $h(k)$, then $h(2)=$ \_\_\_\_\_\_ ; $h(k)=$ \_\_\_\_\_\_ .

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