The good news is that you can pick whatever license you would like for the code that you are writing. You're the author and owner, so you get to pick the license.
But you should still consider a license that is compatible with your dependencies and be aware of how the license of the dependencies can impact your code. So, for example, you can use Apache 2.0 and have a dependency that is GPL 3. Those two licenses are compatible. But be aware that, practically, it means that any one who uses your framework (and the dependencies) will need to license their project under the GPL 3. If you're picking Apache 2.0 because you want a permissive license, that may be a problem for you - even though your code is permissive, the GPL dependency carries through and the person/company using your framework will have to comply with the GPL 3.
The other point to consider is ensuring that your license is compatible with the licenses for your dependencies. For example, the Free Software Foundation's position is that Apache 2.0 is not compatible with the GPL 2. This means that the user of your framework can't comply with both licenses. If they take that sort of thing seriously, it will mean they don't pick your framework.